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Long-term snowpack properties retrieval using satellite microwave emissivities

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LONG-TERM SNOWPACK PROPERTIES RETRIEVAL
USING SATELLITE MICROWAVE EMISSIVITIES
by
Narges Shahroudi
A dissertation submitted to the Graduate Faculty in Engineering
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
The City College of New York
2015
UMI Number: 3671959
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UMI 3671959
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ii Abstract
LONG-TERM SNOWPACK PROPERTIES RETRIEVAL USING
SATELLITE MICROWAVE EMISSIVITIES
by
Narges Shahroudi
Adviser: Professor William Rossow
The main objective of this research is to improve the retrieval of snowpack properties
using passive microwave. First part of this study shows how to better isolate the snow
signature from microwave signal. The second part explains an inversion method to
retrieve snowpack properties using the snow signature. The third part produces a 12-yearlong time-series of seasonal snow parameters (snow depth, density, grain size, SWE) for
the northern hemisphere.
The microwave emissivities used in this study are derived from SSM/I passive
microwave observations by removing the contributions of the cloud and atmosphere and
then separating out the surface temperature. The sensitivity of the effective emissivity to
the presence/absence of snow is evaluated for the Northern Hemisphere. The timeanomaly of differences between effective emissivity at 19V and 85V enabled the constant
effects of land surface vegetation properties to be removed to isolate the snow signature.
The snow detection in comparison with MODIS (Vis/IR) snow cover product agrees for
92% of matched locations and times.
The retrieval is performed by inverting a snow emission model (Microwave Emission
Model of Layerd Snowpack, MEMLS) based on neural network techniques. The model
inputs (Snow properties) and the model outputs (simulated emissivities) were used to
train and test the neural network. Then the surface microwave emissivities (pixels that
iv were identified as snow), the skin temperature, and the ground emissivity (emissivities of
the snow-free pixel) were used as the inputs of the neural network and to retrieve snow
depth, snow density, snow grain size, and liquid water content of the snowpack. An
evaluation of the methodology has been developed to assess the performance of the
retrieval product on different spatial and temporal scales. The method was able to retrieve
dry snow successfully. The method was able to identify wet snowpack. With the retrieved
snow depth and density it was possible to estimate SWE. A comparison of snow depth
and SWE with Chang algorithm showed a 0.9 correlation. In comparison with CMC the
retrieved depth and SWE were higher. It was concluded that the algorithm is well able to
measure dry snow depth and SWE spatially and temporally.
v Acknowledgements
This doctoral dissertation was only possible through the support and guidance of
many extraordinary people. My thesis advisor, Dr. William Rossow, is the one to thank
first and foremost. I am deeply grateful to him for his stimulating motivation and
valuable ideas that helped me complete this work and grow as a research scientist. I am
thankful to him for helping me better develop my methods of scientific thinking. He
provided full support and an extremely enjoyable atmosphere, which has been a great
pleasure to work in. I have enjoyed his guidance and helpfulness in full measure. To him
and to his patience, I am indebted and forever thankful.
I would like to express my sincere respect and deepest gratitude to Dr. Reza
Khanbilvardi. I am grateful to him for providing me the opportunity to learn and
participate in this exciting research topic in a fascinating environment.
I would also like to thank my PhD committee Dr. Peter Romanov, Dr. Barry Gross,
and Dr. Tarendra Lakhankar. Their scientific advice, knowledge, insightful discussions,
and suggestions made this research better.
Special thanks to Cindy Pearl my colleague and friend. Without her help and valuable
advices on programming and data processing I would not be able to complete this work.
Many thanks to the CREST family: Shakila, Sanchia, and Nida for their
administrative and moral support and to my colleagues James, Hamidreza, Marzyeh,
Simon, Jonathan, and Dugwon.
My warmest of emotions are reserved for my parents Sussan and Hossein. Their
everlasting love and support gave me the strength to pass this path and motivated me to
achieve my goals.
The same goes for my aunts, Fatima and Noori. Without their love
vi and support I would not be able to survive in New York. And finally, no small credits
goes to my closest friends, Naseem, Saba, Parmis, Mohsen, Sina, and Ali. I cannot
imagine doing all this without them being always there for me.
vii Table of Contents
ACKNOWLEDGEMENTS ........................................................................................... VI
TABLE OF CONTENTS ............................................................................................ VIII
LIST OF FIGURES ...................................................................................................... XII
LIST OF TABLES .......................................................................................................... XI
1.
INTRODUCTION ..................................................................................................... 1
1.1. BACKGROUND ........................................................................................................ 1
1.2. RESEARCH OBJECTIVES .......................................................................................... 3
2.
LITERATURE REVIEW ......................................................................................... 6
3.
DATA ........................................................................................................................ 12
3.1. LAND MICROWAVE EMISSIVITY (EM) & SKIN TEMPERATURE (TS) .................... 12
3.2. SNOW COVER ....................................................................................................... 14
3.2.1. NOAA Operational Weekly Snow Cover charts (SC): .................................. 15
3.2.2. NOAA Interactive Multisensor Snow and Ice Mapping System (IMS) ......... 15
3.2.3. Canadian Meteorological Centre (CMC) snow depth: ................................ 16
3.2.4. Moderate Resolution Imaging Spectroradiometer (MODIS) snow cover: ... 17
3.2.5. Near real time ice and snow extent (NISE): ................................................. 17
3.3. VEGETATION ........................................................................................................ 18
3.4. SURFACE TYPE...................................................................................................... 18
3.5. TOPOGRAPHY ....................................................................................................... 19
3.6. PRECIPITATION ..................................................................................................... 19
viii 4.
ISOLATION OF SNOW SIGNATURE AND SNOW DETECTION
METHODOLOGY .............................................................................................................
4.1. VARIABILITY OF MICROWAVE EMISSIVITIES ......................................................... 20
4.1.1. Frequency dependence.................................................................................. 20
4.1.2. Vegetation dependence ................................................................................. 23
4.1.3. Temperature dependence .............................................................................. 27
4.2. EVALUATION OF THE SNOW DETECTION ............................................................... 31
4.3. COMPARISONS ...................................................................................................... 34
4.3.1. IMS ................................................................................................................ 35
4.3.2. CMC .............................................................................................................. 35
4.3.3. MODIS .......................................................................................................... 36
4.3.4. NISE .............................................................................................................. 37
4.4. INTERANNUAL VARIABILITY OF SNOW-COVER ..................................................... 38
5.
SNOWPACK RETRIEVAL ................................................................................... 43
5.1. MEMLS ............................................................................................................... 44
5.2. NEURAL NETWORK TECHNIQUE ........................................................................... 51
5.3. NEURAL NETWORK TRAINING USING MEMLS ..................................................... 52
5.4. EVALUATION OF THE METHODOLOGY .................................................................. 57
5.4.1. Neural Network Jacobian and Uncertainties ............................................... 57
5.4.2. Retrieved Parameters (Snow depth) ............................................................. 62
5.4.3. Retrieved Parameters (density, grain size, liquid water content) ................. 70
6.
RESULTS ................................................................................................................. 73
6.1.1. Comparison retrieved snow depth with CMC and Chang algorithm ........... 73
ix 6.1.2. Snow water equivalent (SWE)....................................................................... 77
6.1.3. Interpolation ................................................................................................. 78
6.1.4. Interannual Variability of snowpack parameters ......................................... 80
7.
CONCLUSIONS ...................................................................................................... 86
8.
FUTURE WORK S..................................................................................................... 91
9.
REFERENCES......................................................................................................... 93
x List of Tables
Table 4-1:Statistics of the 7 channels of microwave effective emissivity separated for
snow/snow free surface ............................................................................................. 22
Table 4-2: Percentages of δEM19-85 for different vegetation type showing how much
data falls above .05, below .05 and below TS 0, and below 0.05 and above TS 0 ... 30
Table 4-3: Comparison of the anomaly effective emissivity snow test with IMS, CMC,
and MODIS,NISE ..................................................................................................... 38
Table 5-1:Sensitivity ratios for the input parameters of MEMLS to SSM/I frequencies . 46
Table 5-2:sensitivity test over the modified range ............................................................ 47
Table 5-3: MEMLS snow emission model input range .................................................... 51
Table 5-4:Range of snow-free ground emissivity for each frequency for the training ..... 56
Table 5-5 : comparison of training validation dataset with the outputs of the neural
network ..................................................................................................................... 56
Table 5-6: comparison of the test dataset with the outputs of neural network ................. 57
Table 5-7: The jacobian of the retrieval output with respect to the inputs ....................... 59
Table 5-8: Uncertainty of Depth, Density, Grain size, and water content ........................ 61
Table 5-9:Negative depths ................................................................................................ 67
xi List of Figures
Figure 3-1 Dec 2002 mean effective emissivity map for 3 channels (19H, 37H, 85H),
with the corresponding mean skin temperature ........................................................ 14
Figure 4-1: Global normalized histograms of the effective emissivity for 4 channels
separated for snow and snow free surface using the NOAA snow cover map ......... 21
Figure 4-2: Global normalized histograms of the effective emissivity for 4 combination
channels separated for snow and snow free surface using the NOAA snow cover
map............................................................................................................................ 23
Figure 4-3: Normalized histograms for 2 combination channels of effective emissivities
separated for different kinds of land cover using vegetation classification over
summer 2002 for snow free pixels ............................................................................ 25
Figure 4-4: Anomaly effective emissivity time series for 1 year (2002) for 2 combination
channels for 5 different vegetation type.................................................................... 25
Figure 4-5: Normalized histograms of anomaly effective emissivity of 19V-85V channels
for 5 different vegetation type separated for snow and snow free surface using snow
cover maps. (The y-axis was cut at 8% for a better visualization but their
percentages is shown of the graph) ........................................................................... 27
Figure 4-6: Scatterplots of anomaly effective emissivity of 19V-85V vs. skin temperature
for 2 different vegetation types. Top) snow (cyan) and snow free (red) separated
using NOAA snow flags. Bottom) Snow (cyan) and no snow (red) separated using
the proposed algorithm where class 1a, 1b, 2, and 3 are the disagreement with
NOAA snow flags ..................................................................................................... 30
xii Figure 4-7: Time series of the amount of the snowcover for the snow detection algorithm
for the 12-yr record (1993-2004), NISE for 9-yr (1996-2004), and MODIS for 5-yr
(2000-2004)............................................................................................................... 41
Figure 4-8: Time series of percentage of snow cover over land with snow detection
algorithm, for total snow, Snow detected by effective emissivity, snow detected by
TS. ............................................................................................................................. 41
Figure 5-1: Emissivity vs. Depth where depth varying between 0 and 250 cm for 19 GHz,
37GHz, and 85GHz while density (300kg/m3), grain size (1 mm), temperature
(270K), and liquid water content (0) are constant. ................................................... 47
Figure 5-2: Emissivity vs. grain size where grain size varying between 0.5 to 2.5 mm for
19 GHz, 37GHz, and 85GHz while density (300kg/m3), depth (20 cm), temperature
(270K), and liquid water content (0) are constant. ................................................... 48
Figure 5-3: Emissivity vs. Density where density varying between 100 to 500 kg/m3 for
19 GHz, 37GHz, and 85GHz while grain size (1mm), depth (20 cm), temperature
(270K), and liquid water content (0) are constant (Top). Density (100-500kg/m3)
and Depth (1-50cm) varying while grain size, temperature, and water content are
constant (Bottom)...................................................................................................... 48
Figure 5-4: Emissivity calculated by MEMLS for each frequency. Snowpack was
assumed a single layer (red) and 3-layer (blue) ........................................................ 49
Figure 5-5: Emissivity vs. liquid water content fraction where liquid water content varies
between 1 and 5 % for 19 GHz, 37GHz, and 85GHz while grain size (1mm), depth
(20 cm), temperature (270K), and density (300kg/m3) stays constant ..................... 50
Figure 5-6: Neural Network training/testing chart............................................................ 53
xiii Figure 5-7: Retrieved Depth vs. Test depth for dry and wet snow. .................................. 55
Figure 5-8: neural network chart....................................................................................... 59
Figure 5-9:Difference histogram of calculated and actual emissivities ............................ 60
Figure 5-10: Retrieved depth distribution for snow season 1992-2004, a) all depths, b)
Wet snow removed c) Greenland/ice sheets removed, d) snow pixels with
temperature below 250 removed. .............................................................................. 64
Figure 5-11:Negative depth vs. Temperature ................................................................... 65
Figure 5-12: One pixel time series over a year with mostly positive depth (top) and mix
of positive/negative depth(bottom) ........................................................................... 68
Figure 5-13: : One pixel time series over a year with mix of positive/negative depth
smoothed with a 5 day window ................................................................................ 69
Figure 5-14: : One pixel time series over a year with mix of positive/negative depth with
its corresponding emissivity (19V&85V) and skin temperature .............................. 69
Figure 5-15: Retrieved grain size, density, and liquid water content ............................... 71
Figure 5-16: Wet snow vs. a)precipitation b)skin temperature......................................... 72
Figure 6-1:snow depth map .............................................................................................. 73
Figure 6-2: Retrieved Depth vs. Chang Algorithm ........................................................... 74
Figure 6-3:Retrieved depth vs. CMC depth ...................................................................... 75
Figure 6-4 Retrieved depth vs. edited CMC depth ........................................................... 75
Figure 6-5: Edited CMC depth vs. Chang depth............................................................... 76
Figure 6-6:edited CMC vs. Retrieved depth for grassland over time. Low frequency
variation removed by applying a 5-day high pass filter. ........................................... 77
Figure 6-7: Estimated SWE vs. Chang SWE algorithm ................................................... 78
xiv Figure 6-8: Time series of 1 pixel where the negative depths interpolated ...................... 79
Figure 6-9: Time series of 1 pixel for one year where the negative depths a)interpolated
and b)time averaged .................................................................................................. 80
Figure 6-10: Time series of mean depth for retrieved depth, ........................................... 81
Figure 6-11: Time series of mean snow depth, mean density, mean grain size, and mean
SWE .......................................................................................................................... 83
Figure 6-12:SWE Time anomaly (2003) for SWE=Retrieved Depth x Retrieved Density
(blue) and SWE=Retrieved Depth x Constant Density (red). a) Evergreen forest b)
Tundra c) Deciduous Forest ...................................................................................... 84
xv 1. Introduction
1.1. Background
Snow covers a large area of the Earth during winter, and the knowledge of its
extension and properties is useful for hydrological, meteorological, and climatological
applications. Snowmelt resulting from a climate warming trend would increase the
absorption of solar radiation and produces a positive feedback. Moreover, snow plays a
different role than liquid water in the processes of affecting surface evaporation (latent
heat), soil moisture supply to vegetation, and runoff. Snow acts as a temporary reservoir
of water that is crucial to water supply in many regions (Robinson et al., 1993). Because
of the complex interaction of snow with the landscape and varying atmospheric
conditions, monitoring the spatial and temporal variability of snow properties at relatively
high space-time resolution provides valuable information on surface hydrology and
radiation.
The use of satellite remote sensing for mapping snow cover and measuring snow
characteristics has a long history reaching back to the 1960s. Microwave remote sensing
represents a useful tool for studying the snow distribution and its properties at large scale.
While visible and near-infrared sensors cannot see through clouds, microwave
measurements are largely insensitive to weather conditions and do not require solar
illumination. Microwave sensors are sensitive to snow properties (e.g., phase of water,
mean grain size, density, and snow depth), and many studies have been conducted on the
relationships between snow parameters and electromagnetic signatures (Macelloni,
1 2001;Tedesco, 2005) as well as for retrieving snow parameters from satellite remotely
sensed data (Foster, 1997; Tedesco, 2004). The earth surface emits radiation at
microwave wavelengths (3mm-30cm), while snow cover attenuates and to lesser extent
emits microwave radiation. Deeper snow generally leads to more attenuation and lower
microwave brightness temperature. This principle has been used for decades to obtain
estimates of snow depth or snow water equivalent (SWE) from microwave measurements
(Chang et al. 1987). However, highly accurate estimates of snow depth or SWE from
microwave measurements have remained elusive, especially in high areas with deep snow
such as mountainous regions (Andreadis & lettenmaier 2006).
Passive microwave sensors measure brightness temperature, which, depends on
variations in snow physical properties, variations in the underlying surface, variations in
the atmosphere, and variations in physical temperature. Due to these variations in the
signal, snow depth (and SWE) retrievals algorithm accuracy suffers from significant
complex error sources. Therefore, in order to acquire the snow depth from the microwave
signal, the atmosphere, physical temperature, and underlying surface contributions to the
signal should be removed first. Brightness temperature difference indices (usually 19 - 37
GHz because 85GHz is affected significantly by water vapor in the atmosphere) are
typically applied in inversion algorithms that estimate snow depth. The difference
between 19 and 37 is used to attempt to reduce the effects of disturbing factors, including
influences of physical temperature and forest cover, however, both systematic and
random errors remain considerable. The most important physical snow variation effecting
on microwave emission includes: snow liquid water content (moisture) and snow grain
size (Mätzler, 1999). Different grain sizes lead to high variability in the reflection
2 properties of snow. Liquid water corrupts the sensitivity of observed brightness
temperature as the penetration depth of microwave radiation to snow pack collapses with
increasing moisture. Forward radiative transfer models have arguably advanced to the
point of being able to accurately characterize microwave brightness temperature at the
point scale, given accurate estimates of snow grain size and layering (Lemmetyinen et al.,
2010; Liang et al., 2008; Mätzler, 1999; Tsang et al., 2000; Wiesmann & Mätzler, 1999).
However what is still lacking in the snow studies is a long-term measurement of all the
snow parameters over all surface types.
1.2. Research Objectives
The main objective of this study is to improve microwave measurements of snowpack
properties and to produce a daily Snow Water Equivalent (SWE) climate record to study
the interannual variations of snow properties for climate studies such as flood forecast.
As mentioned above the microwave signal is sensitive to snow properties, however, this
sensitivity is confounded by atmospheric contributions and sensitivity to the variations of
other land surface properties. Therefore first the snow signature should be isolated from
the microwave signal and then the snow signature can be used to estimate snowpack
properties. The objectives of this study in two steps will be:
•
First, to isolate the snow signature from the microwave signal to study the
interannual variation of snow cover.
•
Second, to use the snow signature to retrieve snowpack properties and produce a
daily SWE climate record.
3 To isolate the changes in satellite microwave measurements associated with snow, we
need to account for all the other contributions to the signal to develop a generally valid,
global measurement of snow. In this study land surface emissivities data were used which
were retrieved from the passive microwave brightness temperature (Aires et al., 2001],
see section 3 data), by removing the contributions of cloud and atmosphere and
separating surface temperature. The remaining variability in the emissivities is due to
changes of the land surface characteristics (soil moisture, vegetation density, surface
wetness) as well as the snow properties. To investigate removal of the other non-snow
surface effects from the signal, the space-time variability of land emissivities for different
vegetation categories with and without the presence of snow was examined. The effect of
land is removed from the signal (approximately) by subtracting the mean snow-free
emissivity of each location from its emissivity with snow present.
To retrieve the snowpack properties a trained neural network will be developed which
uses the microwave land surface emissivities derived from SSM/I and the skin
temperature derived from infrared (explained in Chapter 3) as the inputs and retrieves
snow depth, snow density, and snow grain size. In the process of building the neural
network the Microwave Emission Model of Layerd Snow (MEMLS) is used to generate a
dataset to train the neural network.
In Chapter 2 a review of the available snow studies has been conducted. Chapter 3
describes in detail all the datasets, which were used in this study. Chapter 4 explains the
steps of the isolation of the snow signature from the microwave signal and discusses the
results. Chapter 5 describes the development of neural network and evaluates the
4 methodology performance. Chapter 6 evaluates the results retrieved from the neural
network. Chapter 7 concludes this study and Chapter 8 discusses possible future work.
5 2. Literature Review
Unique characteristics of snow, like its high reflectance in the visible part of the
spectrum and its low reflectance in the mid-infrared is the base for most of the wellknown existing techniques for snow detection using the visible (VIS) and infrared (IR)
bands. However, visible imagery is better at detecting snow cover extent than at
quantifying snow characteristics like snow depth or snow water equivalent. Detection of
snow in optical wavelengths still requires clear sky conditions and sufficient daylight. For
this reason and in order to mitigate these disadvantages some studies suggested use of
multiple sensors to measure snow cover. Romanov (2000) automated monitoring snow
cover with the synergy of satellite optical (visible/infrared) and microwave data to map
snow extent and monitor its evolution in time and space. Foster (2011) developed a
blended global snow product that uses Earth Observation System Moderate Resolution
Imaging Spectroradiometer (MODIS), Advanced Microwave Scanning Radiometer for
the Earth Observing System (AMSR-E) and Quick Scatterometer (QuikSCAT or
QSCAT). Only passive microwave can provide useful information on snowpack properties such
as depth, grain size or liquid water content because they can penetrate into the snowpack.
Satellite observations in the microwave spectral range have been used for the global
monitoring of snow cover and surface snow properties for more than three decades. For
example, the remote sensing community uses several data sets from the following
sensors: the Electrically Scanning Microwave Radiometer (ESMR) (1973–1976),
Scanning Multichannel Microwave Radiometer (SMMR) (1978–1987), Special Sensor
Microwave/Imager
(SSMI/S)
(1978–Present),
Advanced
Microwave
Scanning
6 Radiometer–Earth Observing System (AMSR-E) (2002–2011, AMSR-2 2012-present),
and Global Precipitation Measurements (GPM) recently launched in 2014. Using these
sensors, several ways of measuring snow properties have been proposed in the literature.
Existing techniques for the retrieval of snow parameters can be classified as empirical,
and theoretical ones.
Empirical techniques are based on the relationships between measured brightness
temperature and observed snow parameters, which often are expressed in terms of linear
regressions. These algorithms can only estimate one snow parameter (e.g. snow depth or
SWE). The algorithm originally proposed by Chang et al. (1987) estimated snow depth
and SWE from horizontally polarized Scanning Multichannel Microwave Radiometer
(SMMR) measurements. The algorithm has a physical basis the parameterization was
based on forward simulations with a radiative transfer model. This algorithm has been
widely adopted for estimating Snow depth and SWE from different space-borne
microwave radiometers (Armstrong and Brodzik, 2001) including modifications to
account for variable surface and snowpack characteristics (Foster et al., 1997, 1991; Tait,
1998). Armstrong and Brodzik (2002) compared the performance of several traditional
algorithms (Chang et al., 1987, Goodison, 1989; Nagler and Rott, 1992; Rott et al., 1991)
and found large errors at the hemispheric scale when compared to available in situ data.
The general tendency was for the algorithms to underestimate SWE, especially under
deep snow conditions, while algorithm performance broke down completely under wet
snow conditions. Large errors were reported in the hemispheric application of brightness
temperature difference algorithms by Kelly et al. (2003) with lake-rich tundra areas
proving especially problematic for this approach (Derksen et al., 2010; Koenig and
7 Forster, 2004). When applied regionally, land cover specific brightness temperature
difference algorithms have reported lower uncertainties (Derksen, 2008; 2005), although
consistent underestimation of SWE occurs in heavily forested areas and the accuracy
characteristics are subject to inter-seasonal variability due to changes in snowpack
physical properties (e.g. when ice lenses are present).
The second class of inverse algorithms has explicitly sought an inverse solution to
snow emission radiative transfer models, such as by a neural network or some other sort
of iterative search. The available radiative transfer snow emission models includes
Helsinki University of Technology (HUT) model (Pulliainen, 1999, 2001), the
microwave emission model of layered snowpacks (MEMLS) developed at the University
of Bern (Wiesmann and Mätzler, 1999), and the dense-medium radiative theory (DMRT)
(Tsang, 2000).
Tedesco (2004) performed a retrieval of SWE and snow depth by inverting Special
Sensor Microwave Imager (SSM/I) brightness temperatures at 19 and 37 GHz using
artificial neural network ANN-based techniques. The ANN results were confronted with
those obtained using the spectral polarization difference algorithm, the HUT model-based
iterative inversion and the Chang algorithm, by comparing the RMSE, the R2, and the
regression coefficients. In general, it was observed that the results obtained through
ANN-based technique are better than, or comparable to, those obtained through other
approaches, when trained with simulated data.
In another study Tedesco and Kim used a numerical technique based on genetic
algorithms (GAs) to invert the equations of an electromagnetic model based on densemedium radiative transfer theory (DMRT) to retrieve snow depth, mean grain size, and
8 fractional volume from microwave brightness temperatures (Tedesco & Kim, 2006).
Improving the performance of passive microwave retrieval algorithms by means of data
assimilation has also been investigated.
Pulliainen (2006) presents an assimilation technique, which weights passive
microwave data combined with a semi-empirical radiative transfer model, and prior snow
information from ground measurements, with their respective statistical uncertainties.
This technique successfully reduced systematic errors related to the saturation of
brightness temperature difference algorithms when SWE exceeds approximately 120 mm.
Takala (2011) implemented the methodology of Pulliainen (2006) across the northern
hemisphere to exploit the benefits of both conventional measurements and passive
microwave data to produce a Climate Data Record (CDR) for SWE. The approach of
Pulliainen (2006) is enhanced by integrating the methodologies of Hall et al. (2002) and
Takala et al. (2009) to discriminate the region of dry seasonal snow cover and estimate
the date the land surface becomes snow free. Even though accurate estimates can be
obtained for some regions and seasons, SWE estimates tend to show both spatial and
temporal bias in comparison with other algorithms based on the observed spectral
brightness temperature difference (Derksen et al., 2005).
Inverse solutions to characterize snow with brightness temperature have met with
only limited success, not least because multiple sets of snow properties can lead to the
same brightness temperature; the problem becomes more complex with increasing
number of layers. Durand and Liu (2012) developed a new inverse algorithm: a Bayesian
Markov Chain Monte Carlo scheme solved using the Metropolis algorithm. They allowed
the number of snowpack layers itself to be unknown by generating different chains for
9 each possible number of layers, then selecting the optimal chain using a model selection
criterion. They generated synthetic brightness temperature observations using the
microwave emission model for layered snow (MEMLS), and then used the Metropolis
algorithm, MEMLS, and the synthetic observations to estimate the snow properties for
150 snow pits measurements made during the NASA Cold Land Processes Experiment
(CLPX) field campaign. Their method is successfully able to estimate SWE for shallow
snow and less than 4 layers but need prior information for deep snow.
One of the drawbacks of the discussed methods is that they mostly use brightness
temperature in their measurements and hence avoid the atmospheric affect. Using the
land surface microwave emissivities in this study will be an advantage. The land surface
emissivities are retrieved from the passive microwave brightness temperature (Aires et
al., 2001], see chapter 2 DATA), by removing the contributions of cloud and atmosphere
and separating surface temperature. Cordisco (2006) investigated the sensitivity of land
surface emissivities between 19 and 85 GHz for a whole snow season in the Northern
Hemisphere and proposed that the emissivity at 85 GHz strongly reacts to the presence of
snow as soon as it covers the ground. A comparison of the emissivity with brightness
temperature has been done where brightness temperature and emissivity data generated
from (Helsinki University of Technology) microwave emission of snow model were
evaluated with satellite microwave measurements. The comparison of the real
measurements (in-situ and satellite) with the modeled results shows that the scattering
signature shows better results in emissivities rather than brightness temperature data
(Lakhankar, 2012).
The existence of a threshold value for the snow-depth retrieval that is related to
10 the microwave penetration depth at 19 and 37 GHz and the presence of new fresh snow
and wet snow, together with the effect of underlying layer of snow, reduce the accuracy
of these algorithms and restrict the operational applicability of these methods on a global
scale. For this work the emissivity dataset which has removed the atmosphere and
temperature will be used, then the vegetation will be removed in chapter 4, and finally an
inversion approach (neural network) will be used to invert the equations of the snow
emission model (MEMLS) to retrieve multiple snow properties temporally and globally.
11 3. DATA
3.1. Land Microwave Emissivity (EM) & Skin Temperature (TS)
The SSM/I instruments on board the Defense Meteorological Satellite Program
(DMSP) polar orbiters observe the Earth twice daily (typically near dawn and dusk) with
observing incident angle close to 53° for flat a surface and a field-of-view decreasing
with frequency from 43 km x 69 km at 19 GHz to 13 km x 15 km at 85 GHz (Hollinger,
1987]. The SSM/I channels measure brightness temperatures (TB) at 19.3 GHz, 22.2
GHz, 37.0 GHz and 85.5 GHz at vertical and horizontal polarizations except at 22 GHz,
which is only in vertical. SSM/I was the first passive microwave satellite that had
external calibration by viewing a mirror that reflects cold space and a hot reference target
once each scan, every 1.9 seconds (Gentemann, 2010).
Land surface microwave emissivities were determined from the SSM/I brightness
temperatures by removing the effects of the atmosphere, clouds, and rain (Prigent, 1997;
Aires et al., 2001) using ancillary data from ISCCP (Rossow and Schiffer, 1999) and the
NCEP reanalysis (Kalnay et al., 1996). First, the cloud-free SSM/I observations are
isolated using collocated visible/infrared satellite observations from ISCCP. The cloudfree atmospheric contribution is then calculated from temperature-humidity profiles from
the NCEP reanalysis. Finally, surface skin temperature (TS) is taken from ISCCP
(corrected for the original assumption of unit IR emissivity in the ISCCP product using
surface-type-dependent IR emissivities) to determine the surface emissivities for the
seven SSM/I channels. The calculated emissivities can be related to the intrinsic surface
properties independent of atmospheric contributions or the variations of TS. The true
12 emissivity is defined by the normalization of TB by the effective soil temperature
corresponding to the contributions of all the surface layers of the ground weighted by their
attenuation (Wigneron et al., 2008). Hence the emissivities used in this paper are
“effective” values because they are derived from the normalization of TB by the skin
temperature (TS). The spectral gradient of effective emissivities is an index that
approximates the true spectral emissivity difference. The effective emissivities are
determined on an equal area grid equivalent to 0.25° x 0.25° at the equator and are
compiled daily from 1992 to 2004 (recently extended through 2008). For illustration,
monthly mean effective emissivities (EM) are shown in Figure 3-1 for 19V, 37V, and
85V GHz for December 2002. In this chapter EM followed by numbers to indicate
frequency and “H” or “V” to indicate polarization will be used, for example, EM19V or
EM85H. If no letter is given, it means that the statement applies to both polarizations.
EM followed by numbers and letters representing two channels, for example EM19V37V or EM19H-85H, will represent the difference of effective emissivities at two
frequencies. The temporal anomalies of effective emissivity differences as the difference
between the instantaneous effective emissivity difference at a location and a timeaveraged value at the same location will be presented by δEM followed by numbers and
letters representing the two channels, for example δEM19V-37V or δEM19H-85H.
The skin temperature (TS) is the physical temperature of the Earth’s surface (which
can be closer to the canopy top for dense vegetation). The infrared surface brightness
temperature (IR emissivity assumed to be unity) is determined at 3-hour intervals since
1983 over the globe every 30km from a combination of polar and geostationary satellite
(Rossow and Schiffer, 1999). Two values of TS are reported; one based on the IR clear
13 sky radiances from the 5-day composites and one based on any available clear pixel IR
radiances; the former values are a better estimate of TS because the latter values are
slightly cloud contaminated by design (Rossow and Garder, 1993). The ISCCP TS values
are corrected for non-unit emissivities using a land classification to specify IR
emissivities (Zhang, 2004). The corrected ISCCP TS values at 3-hr intervals are
interpolated to match the SSM/I over flight time and mapped to the same 25km grid.
Figure 3-1 Dec 2002 mean effective emissivity map for 3 channels (19H, 37H, 85H), with the
corresponding mean skin temperature
3.2. Snow Cover
The NOAA Operational snow cover product is used to develop the microwave-based
snow detection algorithm and another four products (IMS, CMC, MODIS, and NISE) are
used to evaluate the final product. We focus on the Northern Hemisphere in this study.
14 3.2.1. NOAA Operational Weekly Snow Cover charts (SC):
The operational Northern Hemisphere Weekly Snow and Ice Cover Charts, prepared
by the Synoptic Analysis Branch at National Oceanic and Atmospheric Administration
(NOAA) since 1966 (Dewey and Heim, 1982] are used in the ISCCP cloud analysis to
indicate the presence of sea ice and snow in separating clear and cloudy scenes (Rossow
and Garder, 1993]. The ISCCP version of this information is available in a 1° equal-area
grid at 5-day intervals (interpolated from the original 7-day NOAA product), where
permanent ice cover locations in Greenland and Antarctica are also labeled as snow, but
has been re-projected to the matched ISCCP and SSM/I pixels twice daily on a 25 km
grid for convenience. This product also assumes snow cover for all regions in winter
darkness. This visible-radiant-based snow cover product is used to develop the most
sensitive microwave snow detection algorithm.
3.2.2. NOAA Interactive Multisensor Snow and Ice Mapping System (IMS)
The National Ice Center (NIC) of NOAA/NESDIS produces a daily snow and ice
cover product for the Northern Hemisphere, Continental United States, Alaska,
Afghanistan and Asia/Europe. The data are derived from several data sources, including
the POES AVHRR and AMSU, GOES/Imager, GMS, and Meteosat. In 1997, the
Interactive Multisensor Snow and Ice Mapping System (IMS) became operational, giving
the satellite analysts improved access to imagery and drawing tools. Since the inception
of IMS, the charts have been produced daily at nominal resolutions of 24km and 4km in a
polar stereograph projection (NOAA/NESDIS/OSDPD/SSD, 2004].The 24km version was
used in this study since it better matches with our 25km passive microwave dataset.
15 3.2.3. Canadian Meteorological Centre (CMC) snow depth:
Canadian Meteorological Centre (CMC) compiles the Northern Hemisphere snow
depth analysis data from surface observations. The CMC data set includes daily
observations from 1998-presetn[Brown and Brasnett, 2010]. Real-time snow depth data
were originally acquired from the World Meteorological Organization (WMO)
information system. The analysis is updated every six hours using the method of
optimum interpolation with an initial guess field provided by a simple snow accumulation
and melt model using analyzed temperatures and forecast (six hour) precipitation from
the CMC Global Environmental Multiscale (GEM) forecast model. The precipitation is
assumed to be snow if the analyzed screen-level temperature is less than 0 degrees. In
regions where there are no observations of snow depth, the snow depth shown in the
analysis corresponds to the initial guess field simplified assumptions regarding snowfall,
melt and aging. The CMC daily snow depth analysis is only available at a coarse
resolution of 25 km. The CMC data is remapped to the model grid via a nearest-neighbor
approach, i.e., for any given model grid, the SD value from the nearest grid of the CMC
dataset is assigned. Over most of the Arctic region there are no observations, so the
analysis is based on estimated snow depths from the first guess field. In addition, snow
depth observations over northern Canada tend to be biased to coastal locations with
observing sites at open areas near airports. The snow at these sites tends to be shallower
and to melt out earlier than snow in surrounding terrain. CMC analysis has a tendency
towards early loss of snow cover in the spring due to the shallow bias of snow depths
reported from observing sites that tend to be located in clearings (Brown et al., 2010).
16 3.2.4. Moderate Resolution Imaging Spectroradiometer (MODIS) snow
cover:
NSIDC archives and distributes snow cover and sea ice data products obtained from
the Moderate Resolution Imaging Spectroradiometer (MODIS) sensor on NASA's Earth
Observing System (EOS) Aqua and Terra satellites. The MODIS product contains snow
cover, snow albedo, fractional snow cover, and Quality Assessment (QA). The data are
gridded at 500 m intervals in a sinusoidal map projection over the whole globe. The
results are reported daily at any location that is illuminated and cloud free; thus, over the
wintertime due to the longer nights and cloudy sky, less than 50% of land is observed on
a typical day. The snow cover determinations are based on a snow-mapping algorithm
that employs a Normalized Difference Snow Index (NDSI) and other test criteria (Hall
and Salomonson, 2006).
3.2.5. Near real time ice and snow extent (NISE):
The Near-Real-Time SSM/I-SSMIS EASE-Grid Daily Global Ice Concentration and
Snow Extent product (Near-real-time Ice and Snow Extent, NISE) provides daily, global
near-real-time maps of sea ice concentrations and snow extent. The National Snow and
Ice Data Center (NSIDC) creates the current NISE product using passive microwave data
from the Special Sensor Microwave Imager/Sounder (SSMIS) on board the Defense
Meteorological Satellite Program (DMSP) F17 satellite. Snow extent is mapped
separately using an algorithm developed for Scanning Multichannel Microwave
Radiometer (SMMR) data where, snow depth=1.59 * (TB18H-TB37H) cm (Chang,
1987) and the algorithm was modified for use with SSM/I data as described in
(Armstrong and Brodzik, 2001). NSIDC modified the snow extent mapping algorithm
17 in March 2002, based primarily on a recent study by (Armstrong and Brodzik, 2002). The
snow/ice maps are in EASE-Grid projection with 25km resolution. This product is used
to represents other snow cover products obtained by application of microwave brightness
temperature algorithms (Nolin, 1998].
3.3. Vegetation
A 1° spatial resolution land surface vegetation classification based on Matthews (1983),
distinguishes a large number of vegetation types grouped into 9 classes: rain forest,
deciduous forest, evergreen forest, shrubland, tundra, grassland and desert. Associated
with the vegetation classification is a land use data set that distinguishes five levels of
cultivation intensity, ranging from 0 to 100% for 1° cells. We focus on the five types of
vegetation that experience seasonal snowcover: evergreen and deciduous forests,
shrubland and grasslands, and tundra, which cover together about 80% of the whole
Northern Hemisphere
3.4. Surface type
Surface type is a fixed data product that characterizes the Earth’s surface at each map
location as water or permanent ice shelf or as land in terms of vegetation type or
permanent glaciers. The land vegetation classification is the IGBP-DISC data product
(Loveland and Belward 1997) obtained from the USGS EROS data center. This product
provides the fractional area coverage in a 0.25 degree equal-angle mapping for 17 surface
type (Water, Evergreen Needleleaf Forest, Evergreen Broadleaf Forest, Deciduous
Needleleaf Forest, Deciduous Broadleaf Forest, Mixed Forest, Close Shrubland, Open
Shrubland, Woody Savanna, Savanna, Grassland, Permanent Wetland, Cropland, Urban,
18 Cropland/Natural Vegetation Mosaic, Permanent Snow and Ice (Glaciers), Barren or
Sparsely Vegetated, Permanent Ice Shelf).
3.5. Topography
The Topography dataset is a fixed data product providing a land-water mask together
with topographic height information over land. The product reports land fraction in
percentage, shore distance in km, the mean and standard deviation of topographic height
in meters. The global digital elevation model used to provide land topographic heights is
GTOPO30, obtained from the USGS EROS data center. The standard deviation of
topography height for each 0.25-degree cell tells the roughness of that pixel. The dataset
was used to check to effect of roughness on passive microwave signal.
3.6. Precipitation
The Global Precipitation Climatology Project (GPCP) was established by the World
Climate Research Program to quantify the distribution of precipitation around the globe
over many years. Over land data from over 6,000 rain gauge stations, and satellite
geostationary and low-orbit infrared and passive microwave are merged to estimate
rainfall from 1979 to the present. We use the GPCP-1DD version 6 product that reports
precipitation at one-degree and daily intervals (Adler et al., 2003; Huffman et al., 1997)
19 4. Isolation of Snow Signature and Snow Detection
Methodology
In this section the method of isolation of snow signature from microwave signal on
different surface type using the land surface microwave emissivities is explained. This
section is based on a published paper (Shahroudi and Rossow, 2014).
4.1. Variability of microwave emissivities
4.1.1. Frequency dependence
Land surface microwave effective emissivities (explained in data section 3.1) over
snow exhibit large spatial variability for a given month. For instance, sometimes the land
is fully covered by snow yet the effective emissivity values range between 0.6 and 1. The
same fully snow covered area can have EM19V values between 0.9 and 1, between 0.8
and 1 for EM37V, and between 0.6 and 1 for EM85V. In general higher frequencies
exhibit a larger range of land surface effective emissivities for snow-covered areas.
The frequency distributions of each twice-daily EM value (atmospheric and surface
temperature effects removed) separated between snow-covered and snow-free locations
using the daily snow flag from the NOAA operational product were examined. Table 4.1
is the summary of the statistics for the 12 winter seasons (1993-2004) for the northern
hemisphere showing the minimum, maximum, mean, standard deviation, and mode of the
EM distributions for each channel for snow-covered and snow-free (called land) locations
separately. Figure 4.1 shows the histograms of the individual EM values for four
channels, separated into snow-covered and snow-free locations (the histograms are
normalized to total population of the data in percentages). The table and figure clearly
20 show both the large range of EM values with a concentration of values between 0.85 and
0.95. Notably, the range of both the snow-covered and snow-free effective emissivities
for the lowermost frequencies is similar, with the snow-free mode value shifted to
slightly lower values. The large overlap of the snow-covered and snow-free distributions
shows that EM19 is not very sensitive to the presence of snow and that the effective
emissivities still exhibit large variations with location. At higher frequencies (37 and 85,
H polarization not shown) the range of snow effective emissivities values is larger than
the range for snow-free locations, especially EM85, indicating a much larger sensitivity
to the presence of snow. However, the overlap of the snow-covered and snow-free
effective emissivities is still substantial, especially EM37, so detection of all snowcovered cases is not straightforward.
Figure 4-1: Global normalized histograms of the effective emissivity for 4 channels separated for snow and
snow free surface using the NOAA snow cover map
21 Table 4-1:Statistics of the 7 channels of microwave effective emissivity separated for snow/snow free
surface
Min
Max
Mean
Std
Mode
Snow
Land
Snow
Land
Snow
Land
Snow
Land
Snow
Land
19V
0.931
0.803
1.005
0.990
0.977
0.935
0.028
0.058
0.977
0.954
19H
0.845
0.661
0.975
0.958
0.921
0.875
0.045
0.090
0.949
0.926
22V
0.916
0.797
1.001
0.981
0.962
0.928
0.028
0.055
0.966
0.948
37V
0.794
0.812
0.967
0.966
0.900
0.923
0.047
0.045
0.914
0.940
37H
0.744
0.669
0.940
0.946
0.851
0.872
0.062
0.080
0.886
0.912
85V
0.690
0.839
0.943
0.961
0.813
0.919
0.079
0.036
0.774
0.935
85H
0.648
0.711
0.924
0.946
0.880
0.877
0.088
0.068
0.876
0.912
The similar distributions of EM19 and EM85 for snow-free conditions but the very
different sensitivity of these two channels to the presence of snow suggests looking at
effective emissivity differences to find a distinct threshold for separating the snowcovered from snow-free locations. In particular, Figure 4.1 suggests that the snow-free
values of EM19-37 and EM19-85 will be small, close to zero, but the values for snowcovered locations will be much larger. All possible effective emissivity differences were
examined to look for the combination with the least overlap between the snow-covered
and snow-free distributions. The four smallest overlap percentages from all combinations
are from EM19V-37V (11.4%), EM19H-37H (11.4%), EM19V-85V (10.6%) and
EM19H-85H (10.5%), where the next smallest overlap percentage is around 23%. The
snow-free mean effective emissivity difference is very close to zero for these four
combinations, EM19V-37V (0.003), EM19H-37H (0.005), EM19V-85V (0.002) and
EM19H-85H (0.000). EM19V-22V and EM37V-85V also have (0.001) snow-free mean
but their overlap percentages are 23% and 34% respectively. The same four channel
combination have snow-free standard deviations that are also the smallest where EM19V37V and EM19H-37H are 0.021 and EM19V-85V and EM19H-85H are 0.011. Figure 4.2
shows the snow-covered and snow-free effective emissivity differences for the four best
22 combinations. The figure shows clearly that EM19-85 provides the best separation of
snow-covered from snow-free locations with only a small overlap of the two distributions.
Although from the standpoint of separating snow-covered from snow-free locations, the
two polarizations are not significantly different, the search for the best snow detection
method will be continued by examining results from both polarizations, but only the V
polarization results will be shown henceforth. However in the retrieval of snow properties
all the channels should again be considered to exploit the full information content.
Figure 4-2: Global normalized histograms of the effective emissivity for 4 combination channels separated
for snow and snow free surface using the NOAA snow cover map
4.1.2. Vegetation dependence
To understand the overlapping parts of the histograms in Figure 4.2, the causes of the
range of snow-free effective emissivity differences will be investigated.
The mean
summer maps (June, July, Aug) of the effective emissivity differences, where the same
snowy pixels are snow free, were examined. The statistics show that, when there is no
snow on the ground, the mean summer effective emissivity difference still varies
significantly with surface type and geographically within each surface type (Figure 4.3)
23 with somewhat more difference among different vegetation types for EM19-85 than for
EM19-37. Although the distributions in Figure 4.3 suggest that the snow-free effective
emissivity differences (and effective emissivities, not shown) are associated with
differences in vegetation, the large range of values for each vegetation type shows that
vegetation type provides only a weak discrimination among different locations. In other
words, two different locations classified as the same vegetation type can exhibit variation
of effective emissivity differences (and effective emissivities) that are as large or larger
than the contrast between two different vegetation types. Nevertheless, the vegetation
classification data will be used to separate the effective emissivity difference
distributions, mostly for illustrative purposes. Although the global results using all nine
land cover classes will be examined, the focus is on the five types where there is winter
snow cover: evergreen forest with 20%, deciduous forest with 22%, grassland with 19%,
shrubland with 7%, and tundra with 12% of the total Northern Hemisphere land area. The
sum of these 5 vegetation types covers 80% of the whole Northern hemisphere and will
be counted as our total area for the rest of this section.
The fact that the range of effective emissivity differences within a vegetation class is
as large or larger than the difference between vegetation classes suggests a different
approach for reducing the geographic variations of the effective emissivities of the land
surface underlying the snow cover. For each location (at 25 km intervals) the temporal
anomaly of the effective emissivity differences (δEM) with respect to its summer-season
mean value was calculated (Equation 4-1).
δEM19-37 = EM19-37 – [EM19-37]
(4-1)
δEM19-85 = EM19-85 – [EM19-85]
24 where [] indicates the average over the summer season at the same location.
Figure 4-3: Normalized histograms for 2 combination channels of effective emissivities separated for
different kinds of land cover using vegetation classification over summer 2002 for snow free pixels
Figure 4-4: Anomaly effective emissivity time series for 1 year (2002) for 2 combination channels for 5
different vegetation type.
25 Figure 4.4 shows the annual progression of δEM19-37 and δEM19-85 averaged for
each of the five vegetation types. There are three notable features in this figure. First, the
variability of δEM during the summer is extremely small compared with the seasonal
variations produced by snow. In other words, the background land surface values of δEM
are very stable in time. Second, that the average δEM values for snow-free conditions are
so small indicates that we have eliminated most of the “non-snow” variability using these
quantities. Third, we note that the effects of snow are larger for δEM19-85 than for
δEM19-37 as might be expected. Finally the figure shows that the effect on the δEM
values is largest for the tundra and evergreen locations.
The (approximately) 10% overlap of the snow-covered and snow-free distributions of
effective emissivity difference has been reduced by about a factor of 3-4 for the anomaly
emissivity difference. The reduction is largest for EM19-85 as expected. By subtracting
the mean summer effective emissivity difference from the daily effective emissivity
differences in winter, we are taking out a constant offset approximately representing the
effect on the microwave signal from the underlying land surface. Since the microwave
sensitivity to the underlying surface can disappear for higher frequencies and larger snow
depths (50 to 100 cm at 37 GHz depending on density and grain size (Liang et al., 2008),
this approach can underestimate the snow signal for deeper snowcover. Nevertheless,
variations in δEM should have only the snow signal without the geographic variations of
vegetation properties. The anomaly values for snow free areas become much smaller and
closer to zero (generally less than 0.05) and the snow signal becomes more distinct.
The histograms (normalized by total sample size) of δEM19-85 for all 5 vegetation
types for the whole 12-yr record are shown in Figure 4.5 to illustrate the separation of
26 snow-covered and snow-free signals that has been achieved. The range of snow-free
values is noticeably smaller and concentrated near zero. The range of snow-covered
values is shifted to larger values and a clearer separation of snow/snow free is apparent.
Only about 1% of the snow-free δEM19-85 values are above 0.05. It was concluded that
any value of δEM19-85 above 0.05 is snow-covered, whereas values below 0.05 are still
a mix of snow-covered and snow-free locations.
Figure 4-5: Normalized histograms of anomaly effective emissivity of 19V-85V channels for 5 different
vegetation type separated for snow and snow free surface using snow cover maps. (The y-axis was cut at
8% for a better visualization but their percentages is shown of the graph)
4.1.3. Temperature dependence
The overlapping snow/snow free parts of the δEM19-85 distributions for evergreen,
deciduous, grassland, shrubland, and tundra represent relative fractions of about 3%, 6%,
27 11%, 8%, and 3%, respectively, showing that deciduous and grassland cause the most
ambiguity in snow detection in the microwave. Therefore, additional information that
might help detect snow over these surfaces was acquired. The other quantity obtained in
the retrieval of the surface effective emissivities is the corresponding skin temperature
(TS): since only the clear scenes is used in this study, this value comes from collocated
and coincident IR radiance retrievals from the ISCCP data product. One thing to check is
whether the effective emissivities are correlated with temperature, that would indicate
some residual dependence or whether the skin temperature data can be used as extra
information together with the effective emissivities to detect snow.
To explore this possibility, it is shown in Figure 4.6a and 4.6b the scatter plots for
deciduous and grassland for 1 day (as an example) of the values of δEM19-85 vs. TS,
where the color-coding indicates how the operational NOAA product labels each
location. As it can be seen there are some locations with δEM19-85 < 0.05 and TS < 0C
that are labeled as both snow-covered and snow free but this is also true for TS > 0C;
likewise for δEM19-85 > 0.05 there are both snow-covered and snow-free locations both
above and below TS = 0C. The figure shows one day of the data for clarity but Table 4.2
shows the statistics for daily data over all 12-winter seasons, showing the percentage of
the snow-covered and snow-free pixels according to the NOAA product for each
combination of δEM above and below 0.05 and TS above and below 0C for the 5
vegetation types. As already shown, almost all locations with δEM19-85 ≥ 0.05 are
labeled as snow-covered and almost all locations with δEM19-85 < 0.05 and TS > 0C are
labeled as snow free. The key result is that almost all locations with δEM19-85 < 0.05 but
TS < 0C are also labeled as snow-covered. The worst disagreement according to the
28 NOAA product is for deciduous forests, but this case is also difficult for a mostly-visibleimage-based analysis.
Thus, the snow detection procedure was modified as defined by Equation 4-2.
If δEM19-85 ≥ 0.05
=> Snow
If δEM19-85 < 0.05 & TS <0 => Snow
(4-2)
If δEM19-85 < 0.05 & TS ≥0 => No Snow
Equation 4-2 is applied to the data and the results compared with the operational
NOAA snow cover product. Figure 4.6c and 4.6d illustrates these new results for one day
over grassland and deciduous; Table 4.2 contains the statistics for all 12 years. The colors
now indicate the following: cyan means both datasets agree that the location is snowcovered and red means both datasets agree that the location is snow-free. There are four
classes of disagreement: Class 1a (yellow) are locations with δEM19-85 > 0.05 and TS >
0 that we call snow-covered that are called snow-free by the NOAA product, Class 1b
(black) are locations with δEM19-85 > 0.05 and TS < 0 that we call snow-covered that
are called snow-free by the NOAA product, Class 2 (magenta) are locations where
δEM19-85 < 0.05 and TS < 0C that we call snow-covered but the NOAA product labels
as snow-free, and Class 3 (green) are locations where δEM19-85 < 0.05 and TS > 0C that
we call snow-free but the NOAA product labels as snow-covered. About 50% to 90% of
the pixels for each of the vegetation types in winter have δEM19-85 above 0.05 where
Shrubland is the lowest (47%) and Tundra is the largest (94%) and the combination of all
vegetation is 63%. Around 5% to 30% have δEM19-85 below 0.05 and TS below zero
and around 10% to 45% have δEM19-85 below 0.05 and TS above zero. The
29 disagreement frequency for the combination of all vegetation types are 1% for class 1a
and 1b, 3% for class 2, and 1.6% for class 3 (table 4.2).
Figure 4-6: Scatterplots of anomaly effective emissivity of 19V-85V vs. skin temperature for 2 different
vegetation types. Top) snow (cyan) and snow free (red) separated using NOAA snow flags. Bottom) Snow
(cyan) and no snow (red) separated using the proposed algorithm where class 1a, 1b, 2, and 3 are the
disagreement with NOAA snow flags
Table 4-2: Percentages of δEM19-85 for different vegetation type showing how much data falls above 0.05,
below .05 and below TS 0, and below 0.05 and above TS 0
Vegetation
Evergreen
Deciduous
Grassland
Tundra
Shrubland
All Vegetation
Flag
Snow
No Snow
Snow
No Snow
Snow
No Snow
Snow
No Snow
Snow
No Snow
Snow
No Snow
δEM19-85> 0.05
δEM19-85<0.05
TS<0
δEM19-85<0.05
TS>0
78.35%
0.82%
9.08%
0.66%
0.81%
10.29%
53.79%
2.15%
17.37%
8.04%
0.31%
18.33%
45.91%
1.08%
30.75%
3.72%
2.72%
15.81%
93.37%
0.52%
24.25%
0.84%
61.99%
1.07%
5.67%
0.14%
25.62%
4.43%
17.27%
3.04%
0.09%
0.21%
5.48%
39.39%
1.67%
14.95%
30 4.2. Evaluation of the snow detection
As discussed in the previous section and shown in table 4-2 there is agreement for
about 90% of all locations between the proposed algorithm and the NOAA product and
about 10% disagreement.
For snow detection, deciduous is the most problematic
vegetation type and for the snow-free detection, shrubland is the most problematic one.
Therefore, although the effect of vegetation was removed from the effective emissivity it
can still disturb the signal. The uncertainty in the ISCCP temperatures at high latitudes is
about ± 2-3K under clear wintertime conditions (Moncet et al., 2011; Prigent et al.,
2003), so we first test the sensitivity of the disagreements by changing the skin
temperature threshold to +2°C or -2°C instead of zero. If the threshold is +2°C instead of
0°C, the snow-detection disagreement (class 2) for all vegetation increases by 3% and the
snow-free detection disagreement (class3) decreases by 1%. If the threshold is changed to
-2°C the snow-detection disagreement (class 2) for all vegetation decreases by 3% and
the snow-free detection disagreement (class3) increases by 1%. Therefore, there is about
6% change in the disagreement percentages for the snow-detection and 2% for snow-free
detection when the temperature threshold is changed. In other words, about half of the
disagreements could be due to the TS errors.
The behavior of the 10% of cases that disagree was studied individually for each of
the four classes is examined. To aid in the study of these pixels, we bring in precipitation
information from GPCP. Three situations were found that explained most of the
disagreement in the four classes: a) rapid melt/freeze events, b) precipitation, and c) ice
cover labeled as snow. These three types of situation explain about 90% of the
31 disagreements, that is 9% of the 10%. The pixels which did not fall into any of these
situations (about 1%) are called “Un-explained“.
The melt/freeze situation accounts for the largest percentage of all the four
disagreement classes and all vegetation types. The day-to-day variations of IR skin
temperature of the pixels in each class centered on the day of disagreement was
examined. A melt event happens when TS of a pixel is below zero on one day and is
suddenly above zero on the next day and a freeze event happens when TS of a pixel is
above zero on one day and is suddenly below zero on the next day. This causes the snow
to melt (melting does not have to be complete) or surface water to freeze suddenly;
therefore the surface dielectric constant on day one will be different from that on the next
day. Since the dielectric properties of liquid and frozen water at microwave frequencies
are very different, the change of phase produces a substantial variation on surface
effective emissivity. Therefore, even though the temporally sparse visible observations
label these pixels as snow-covered or snow-free over these few-day intervals (remember
that a visible-image-based snow detection obtains results only under clear conditions,
which limits the time sampling to a scale of a few days), the microwave observations
sense the changes (melt or freeze). More than 50% of each disagreement class is
explained by rapid melt/freeze events; Shrubland has the highest and Tundra the lowest
percentage in this situation.
The situation with the next largest percentage after melt/freeze is precipitation. The
GPCP daily precipitation data was used to check if there was a precipitation event at
those pixels on the specific days of disagreement. Between 5% and 30% of the pixels in
each of the classes can be explained by contamination by rainfall or snowfall events. The
32 microwave effective emissivities used in this study are obtained under the clear sky
conditions as indicated by the coincident ISCCP cloud product. However, each 0.25degree map grid cell contains only a one-pixel sample from ISCCP; this sample is a
single pixel about 5 km across, so the ISCCP dataset only samples about 4% of the 0.25degree area. Thus, it is possible on rare occasions that the low areal coverage by ISCCP
and the low spatial and temporal resolution of GPCP (1°, daily) can allow for some
instances of coincident clear conditions and precipitation. The GPCP data does not say if
the precipitation is in form of rain or snow. If the temperature of that pixel is above about
-5 C the precipitation (about 2/3 of the precipitation error falls into this category) is most
likely in the form of rain and which will change the surface dielectric constant, causing
an error in the snow detection. If the temperature of that pixel is below about -5 C the
precipitation is most likely in the form of snow (about 1/3 of the precipitation error falls
into this category) so the sensitivity of the higher frequency microwave to falling snow
(Skofronick-Jackson et al., 2004) can produce an error in the snow detection. Evergreen
and grassland have the largest percentages of this situation (about one fifth to one third of
the disagreements) but this situation does not occur over Tundra.
Another situation is when δEM19-85 < 0.05 and TS is very cold, below -20° C. These
pixels are called snow-covered according to equation 2. The NOAA snow cover product
labels some of these pixels ice-covered and some of them as snow-free. Including the ice
cover part of the NOAA dataset accounts for more than 50% of the pixels with very cold
TS. The ice product labels Greenland (and Antarctica) as permanent ice where there
could be snow on the ice. However, as the summertime mean EM difference, is actually
33 representative of ice cover, the values of δEM19-85 do not indicate snow-cover. Tundra
has the largest percentages in this situation.
The un-explained situation is where none of the above explanations applies. This
situation occurs about 5% to 12% for each disagreement class with Shrubland and
Grassland having the highest percentages (equalized to 1% of the total dataset). Some of
these cases can be explained by the mismatch of temporal and spatial resolutions as
discussed in section 2, where it was shown that about 2-4% of the disagreements can be
explained by these mismatches and TS errors (Moncet et al., 2011)
Of the 10% of cases where there was apparent disagreement about the presence or
absence of snow, the rapid melt/freeze events explained the largest percentage (more than
half) of these and the un-explained situations accounted for less than 10% (1% of the
total data). Deciduous and Grassland have the largest disagreement for snow detection
(class 1a, 1b, and 2) and Shrubland has the largest disagreement for snow-free detection
(class 3), mostly due to rapid melt/freeze events. Class 1b (where δEM19-85 > 0.05 and
TS < 0) has a very small percentage (less than 1% of the total data) compared to the other
classes and can be neglected. There are number of studies on melt/freeze of snow during
melting seasons using visible, passive and active microwave data (Foster et al., 2011;
Royer et al., 2010]. There is about 90% agreement between the snow detection algorithm
(equation 4-2) and the NOAA product. To confirm this agreement, the snow detection
results are next compared with other available snow cover datasets.
4.3. Comparisons
The results of our snow detection procedure were compared with three different
datasets: the daily NOAA IMS snow cover (a mixed visible and microwave based
34 product), the Canadian Meteorological Center (CMC) snow depth (a completely satelliteindependent product), MODIS snow cover (a visible-NIR based product), and another
microwave product Near-Real time ice and snow extent (NISE) (a microwave brightness
temperature product). The accuracy of these maps is not known either but the techniques
used to map snow cover in the various maps are very different. Each of these snow cover
maps were also compared to each other.
4.3.1. IMS
The IMS product is manually created by a satellite analyst looking at all available
satellite imagery, several automated snow mapping algorithms, and other ancillary data.
For snow extent, they rely primarily on visible band satellite imagery. The analyst begins
with a previous day’s map as a first guess and changes it only if there is data available for
that day. Thus the effective time resolution is a few to many days. We compared the daily
IMS snow product with our snow detection algorithm snow product for five available
matching years (2000-2004). As it is shown in table 4.3 about 66% of the data agree for
snow and about 16% agree for no snow. There is about 18% disagreement, where some
of it can be explained by the filling of the data with the pervious available observation.
4.3.2. CMC
Snow depth data from CMC were compared with our results showing about 74%
snow agreement, 11% no-snow agreement, and 15% disagreement. The disagreement
may be increased by the fact that the CMC data are station (point) data, whereas the
satellite data has a 25 km footprint (Table 4.3). The IMS and the CMC are in good
agreement with each other at about 91%.
35 4.3.3. MODIS
The MODIS snow product has a lot of missing data on a given date because pixels
during night and cloudy sky conditions have no snow report. More than 50% of the
MODIS data in the northern hemisphere during the snow season fall into the night and/or
cloudy category each day, where snow detection is not possible. Only the available pixels
with each other at each day for 5 years (2000–2004) were compared in such a way that all
the 500 m pixels of MODIS were averaged in a 25 km pixel (matched with the passive
microwave) and if the snow percentage was more zero the pixel was called snow. This
comparison showed 58% of the snow agrees, 33.47% of the no snow agrees, and 8%
disagreed (Table 4-3). Some of the disagreements can be due to the spatial resolution
differences. Since MODIS has much higher resolution than the microwave and it reports
snow cover percentage for each pixel, another comparison was done in order to check
that when the MODIS snow coverage is less 100% what would the snow detection
algorithm call the pixel. Looking at the 500 m resolution MODIS pixels it was found that
only 6% of the snow-covered pixels have values between 1 and 99% and when the
500mMODIS pixels are averaged to 25km pixels this percentage only increases to 11%.
When the MODIS snow coverage is 100% the snow agreement with the snow algorithm
is 98%, and as the snow coverage decreases the agreement decays down to 60% for snow
coverage below 25%. From these statistics it can be said that first, averaging the 500
pixels to 25 km only increases the partial snow coverage by 5%. Second, the pixels with
less than 25% snow coverage are the largest group, which are still very rare situations.
Third, of this 11% of the pixels with partial snow coverage our snow algorithm detects
snow pixels between 60 and 80% of the time. Comparing the MODIS snowcover with the
36 CMC and IMS data using only available pixels of the MODIS, there is about 36% of
snow agreement and 53% of no snow agreement. The remaining 10%, which disagrees,
again can be due, in part, to the different spatial resolutions of the datasets.
4.3.4. NISE
The NISE data were compared with our results showing about 37% snow agreement
and 41.8% no-snow agreement. There is 18% disagreement with the snow detection
where 12% of it falls into the condition of δEM19-85 < 0.05 and TS<0 which will be
called snow with our detection but are called no-snow with the NISE products. Most of
the disagreement is with the TS in the detection and about half of this 12% is due to the
melt/freeze transition. This data is derived from SSM/I microwave using an algorithm
(Armstrong and Brodzik, 2001] that uses the brightness temperature difference of two
channels (19H-37H). Their study demonstrates that their algorithm underestimates snow
extent in presence of shallow snow; however it tends to overestimate snow extent (both
wet and dry) in various locations (Nolin, 1998]. 85GHz which was used in the snow
detection algorithm can see shallow snow better. Comparing NISE and MODIS there is
83% agreement between them. MODIS is the visible-infrared based snow product that
agreed best (92%) with the snow algorithm, which shows the snow cover from the
algorithm is a more sensitive microwave-based algorithm than NISE.
37 Table 4-3: Comparison of the anomaly effective emissivity snow test with IMS, CMC, and MODIS,NISE
(IMS)
CMC
MODIS
NISE
Flag
Snow
No Snow
Snow
66.16
4.26
No Snow
Snow
13.71
15.84
73.94
9.04
5.77
11.22
No Snow
Snow
No Snow
Snow
No Snow
58.16
6.42
36.69 18.31
1.92
33.47
3.10 41.8
4.4. Interannual Variability of snow-cover
One motivation for producing an accurate snow detection dataset, besides using it to
study snowpack properties and behavior, is to be able to study the slow interannual
variations of snow cover that are not only indicators of climate change but also an
important positive feedback on global warming as reduced snow cover leads to increased
solar heating. To understand the atmospheric and surface processes involved requires
resolving the time variations at scales commensurate with weather events. Such studies
will have to extend the daily (or even twice-daily) microwave snow cover detection to
retrievals of the physical properties of the snow and combine these results with other data
products quantifying weather events.
The time series in Figure 4.7 shows the number of snow-covered pixels for each day
divided by all the pixels for the five vegetation types in the Northern Hemisphere,
normalized by the maximum value in the record for the our snow signal, MODIS, and
NISE. There are no changes from 1993 until the winter of 2001-2002 when there is a
10% decrease in the maximum snow cover extent as well as an increase in the summer
38 2002 minimum extent. Over the next few years, the maximum extent slowly increases
towards its prior values but the summertime minimum extent remains the same.
The timing of this apparent change in snow cover and temperatures is unfortunate,
since there is a known increase of the ISCCP global monthly mean TS values by a little
less than 3 K between September and October 2001 that is produced by a change in the
atmospheric temperature-humidity product (TIROS Operational Vertical Sounder,
TOVS) used by ISCCP to retrieve surface skin temperatures (Zhang, 2004]. Since the
effect on surface temperature depends on the changed atmospheric absorption of infrared
emission from the surface as well as atmospheric emission, both of which depend on the
water vapor abundance, the magnitude of the change in high latitude wintertime TS
values is weaker than the global mean change. To investigate whether this affects our
results, we first examined maps of monthly temperature differences (we are looking for a
bias) between September and October in 2000, 2001 and 2002. We find differences in TS
< 5 K in lower latitudes but much smaller changes at higher latitudes: the decrease of TS
from September to October (difference of monthly averages over the area for the five
vegetation types) is about 8 K in 2000 and 7 K in 2002, when there is no systematic
change of the TOVS product between months. However, in 2001, this change is only a
little over 5 K, suggesting that the TOVS change may have reduced the seasonal decline
of TS by up to 3 K – the change of TS in wintertime will be smaller still.
A spurious change in TS can affect our snow detection in two ways. First, since we
use a TS test as part of the detection algorithm, any shift of TS could induce a bias of
snow cover. The threshold sensitivity test we described earlier in Section 4.2 shows that
snow extent would change by only about 2-3% for a 2 K change in TS. However, Figure
39 4.8 shows the fraction of the total snow cover detected by the effective emissivity-only
and the temperature thresholds (Equation 4-2), demonstrating that not only is most of the
snow detected by the temperature-independent threshold on δEM19-85 but also that all of
the decrease in snow cover extent comes from the effective emissivity part of the
algorithm. So the TS change from ISCCP is not large enough to explain the 10% decrease
in snow cover extent. The second way that TS can affect our results is in the retrieval of
the microwave effective emissivities. However, the decrease in δEM19-85 comes entirely
from the EM85 (not shown). The fact that EM85 changes, but EM19 does not, is
inconsistent with a temperature-induced error in the microwave retrieval which requires
the same physical temperature for all microwave channels. Thus, if a change in EM is to
be associated with a change in TS, all channels should exhibit similar changes. Any
residual effect of the biased TS values input to the retrieval from ISCCP is further
mitigated by using EM differences in our detection algorithm. Thus, we conclude that the
sudden change of the ISCCP TS values between September and October 2001 cannot
explain the decreased snow cover extent that we obtain in the following winter of 20012002 relative to previous winters. Moreover, the interannual evolution of the ISCCP TS
values after 2001 shows no significant trends to explain the subsequent slow increase of
wintertime snow cover extent. We also note the MODIS (VIS/IR) snow cover product
shows a similar decrease but by about 7%, and the NISE (passive microwave) data shows
about 4% decrease (Figure 4.7). The other two snow products, IMS and CMC, do not
exhibit any changes (not shown). More investigation of the possible variations of snow
cover extent is warranted to verify this result.
40 Figure 4 7: Time series of the amount of the snowcover for the snow detection algorithm for the 12-yr
record (1993-2004), NISE for 9-yr (1996-2004), and MODIS for 5-yr (2000-2004)
Figure 4-8: Time series of percentage of snow cover over land with snow detection algorithm, for total
snow, Snow detected by effective emissivity, snow detected by TS.
The algorithm produces a more sensitive microwave detection of snow and is in 92%
agreement with MODIS, which is a very high-resolution visible/IR snow cover product.
The product has isolated the snow part of the signal (approximately) which can now be
used to characterize the physical snowpack properties such as snow depth, snow density,
snow grain size, snow water equivalent, etc. In the next chapter a retrieval method will
be explained to estimate the snow properties. The effective emissivities, the summertime
ground emissivity, and the skin temperature associated with each pixel will be used in the
41 retrieval and only snow-covered pixels according to equation 4-2 will be entered for the
retrieval. During the evaluation of the retrieval method in chapter 5 the temperature
threshold for equation 4-2 will be change in a way that if the anomaly emissivity
difference is more than 0.05 and the skin temperature is less larger than 250K the pixel
wont be considered as snow covered and it will be flagged as ice.
42 5. Snowpack Retrieval
The objective of this chapter is to develop a technique to retrieve snowpack properties
by using the passive microwave emissivities (the isolated snow signature, which were
formed in chapter 4). An inversion technique (neural network) will be developed which
inverts the snow emission model (MEMLS) based on radiative transfer theory to retrieve
snow depth, snow density, snow grain size, and liquid water content.
The ability of snow emission models to accurately predict microwave emission of a
snowpack is complicated because of the variations of the snowpack properties, especially
stratigraphic variations and the wetness of snow.
Therefore, there is a need for a
multilayer medium model that account for stratigraphic variations, and also has the
ability to model brightness as a function of wetness. It was found that The Microwave
Emission Model of Layered Snowpack (MEMLS)
(Wiesmann and Mätzler, 1999)
considers a layered structure of the snowpack and takes into account the liquid water
percentage of each layer. Other snow emission such as HUT and DMRT do not have the
advantage of both characteristics. HUT model has the advantage of including the
atmosphere, soil, and vegetation contribution when calculating the brightness
temperature, but does not consider the liquid water content of the snowpack. Muñoz
(2014) suggested an improvement to the HUT model by proposing an equation to predict
wetness. It was decided to use MEMLS for this study however other models can be
considered for future studies.
There are various techniques proposed for solving inverse equation of radiative
transfer model in remote sensing. Neural nets are particularly appealing for the inversion
of atmospheric remote sensing data, where relationships are commonly nonlinear and
43 non-Gaussian. For example the relation between microwave measurements and the snow
parameters is highly nonlinear. Very few studies have used neural network models for
snow depth and SWE retrieval from SSM/I where the neural network training sets were
generated by using simulated brightness temperature obtained from a physical model.
Neural networks have better performance than linear regression models because of their
ability to approximate nonlinear functions and having the advantage of capturing multivariable effects. Another important benefit of neural network models is that they can
retrieve a very large amount of data in a short time. Neural network models are datadriven models providing an input–output mapping through a supervised learning process
that modifies the synaptic weights between the neurons to reduce gradually the difference
between the desired response and the response from the network.
In this chapter a feed-forward multilayer perceptron, which consists of an input layer,
one nonlinear hidden layer, and a linear output layer will be trained using snowpack
properties, and the emissivities generated by MEMLS emission model. The neural
network then retrieves snow depth, snow density, snow grain size, and liquid water
content by taking the microwave land surface emissivities derived from SSM/I and the
skin temperature derived from infrared (explained in chapter 3) as its inputs.
5.1. MEMLS
The Microwave Emission Model of Layered Snowpack (MEMLS) is based on the
studies carried out by (Wiesmann and Mätzler (1999)]. The model considers snowpack as
a stack of horizontal layers and uses a combination of empirical relationships and
physical properties to characterize the radiative properties of each snowpack layer. The
main input parameters of MEMLS (besides frequency and incidence
44 Angle) are surface reflectivity and from vertical profiles of the snowpack thickness,
correlation length of grain size, density, liquid water content and temperature. The inputs
are then approximated by a finite number of homogeneous layers to obtain the
reflectivities at each layer interface, and the propagation parameters within each layer.
The Radiative transfer within each layer is described by a 6-flux model with given
absorption and scattering coefficient. The scattering and absorption coefficients can be
calculated by empirical functions of grain size and density (Wiesmann &Mätzler, 1999).
The scattering coefficient increases as a function of increasing grain size and decreases as
a function of increasing density. Qualitative evaluation of MEMLS accuracy has been
reported in Durand (2008). Correlation length is related to size, shape, and volumetric
distribution of snow grains (Mätzler, 2002). It has been shown that to first-order, a
logarithmic relationship holds between correlation length and grain size (Durand et al.,
2008). Using the data of Mätzler (2002), assuming a spherical shape for grain size,
correlation length = Grain size x 0.16. The term grain size will be used for the rest of
this text for this measurement.
A parameter sensitivity test was done to study the model. The range of each
parameter was chosen according to field measurement studies in the literature (Dietz,
2012) first but later it was adjusted for the neural network training. The surface
reflectivity and surface temperature were both assumed 0 for this test. The ratio of the
difference between the maximum and minimum of the emissivity divided by the
difference between maximum and minimum value of the parameter (Equation 5-1) shows
the sensitivity of each SSM/I frequency channels in respect to each snow properties
(Table 5-1)
45 Ratio= (EMmax-EMmin) / (Xmax-Xmin)
(5-1)
Where X is the snow parameter and EM is the emissivity.
Table 5-1:Sensitivity ratios for the input parameters of MEMLS to SSM/I frequencies
Depth
(0-300) cm
19V
19H
37V
Density
(100-500)(Kg/m3)
Grain size
(0.5-2) mm
Temp
(240-275) K
Water Fraction
(0-5%)
0.07
0.06
0.06
0.06
0.57
0.53
0.0007
0.0006
0.037
0.035
0.08
0.24
1.61
0.0013
0.099
37H
0.08
0.23
1.51
0.0013
0.096
85V
85H
0.20
0.41
2.41
0.0005
0.162
0.18
0.40
2.30
0.0005
0.159
From table 5.1 it can be said that grain size is the most sensitive parameter to all the
frequencies. Depth, density, and water fraction are more sensitive in higher frequency
than lower. Temperature is the least sensitive properties compare to the other ones. In
order to further examine how the emissivities fluctuate with changes in each parameter
the model was ran by varying one parameter at the time and keeping the others constant
at the time.
Depth was varied between 0 and 250 cm while density (300k/m3), grain size (1 mm),
temperature (270K), and liquid water content (0%) stayed constant (figure 5-1). The
emissivity values in all frequencies decreases as snow depth increases, although the
magnitude of change is smaller in lower frequencies. The signal looses sensitivity after
20cm of snow depth for 85Ghz. In 37Ghz and 19GHz the signal looses sensitivity after
150cm and 300cm of snow depth respectively. The parameter sensitivity test was done
over these new ranges the same way as in equation 5-1 (Table 5-2). As it as expected
85Ghz has higher sensitivity when the depth is between 0 and 20cm than when the depth
is higher. From the sensitivity analysis it can be said that all the frequency channels are
46 providing unique information at different snow depth and the use of all of them together
is essential for retrieval purposes.
Table 5-2:sensitivity test over the modified range
19V
19H
37V
37H
85V
85H
Depth
(0-300) cm
0.07
0.06
0.08
0.08
0.20
0.18
Depth
(0-150) cm
0.11
0.10
0.16
0.15
0.39
0.37
Depth
(0-20) cm
0.19
0.17
0.58
0.54
2.59
2.43
Figure 5-1: Emissivity vs. Depth where depth varying between 0 and 250 cm for 19 GHz, 37GHz, and
85GHz while density (300kg/m3), grain size (1 mm), temperature (270K), and liquid water content (0) are
constant.
Grain size was varied between 0.5 and 2.5 mm while density (300k/m3), depth (20
cm), temperature (270K), and liquid water content (0%) stayed constant (figure 5-2). The
emissivity decreases as the grain size increases and again the magnitude of change is
larger in higher frequencies.
Snow density varied between 100 and 500 kg/m3 while depth (20 cm), grain size
(1mm), temperature (270K), and liquid water content (0%) stayed constant. The
emissivity in all the channels both polarizations increase as the density increases.
Looking at the change of depth and density at same time shows that the magnitude of
47 change in density at 85 GHz is much larger when snow depth is less than 10cm (Figure
5.3).
1
EM19
EM37
EM85
0.9
0.8
Emissivity
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.5
1
1.5
2
2.5
Grain Size (mm)
Figure 5-2: Emissivity vs. grain size where grain size varying between 0.5 to 2.5 mm for 19 GHz, 37GHz,
and 85GHz while density (300kg/m3), depth (20 cm), temperature (270K), and liquid water content (0) are
constant.
1
EM19
EM37
EM85
Emissivity
0.8
0.6
0.4
0.2
100
150
200
250
300
350
400
450
500
density(kg/cm3)
Emissivity 85V
Density(kg/m3)
100
200
0.8
300
0.6
400
0.4
500
0.2
0
5
10
15
20
25
Depth (cm)
30
35
40
45
50
Figure 5-3: Emissivity vs. Density where density varying between 100 to 500 kg/m3 for 19 GHz, 37GHz,
and 85GHz while grain size (1mm), depth (20 cm), temperature (270K), and liquid water content (0) are
constant (Top). Density (100-500kg/m3) and Depth (1-50cm) varying while grain size, temperature, and
water content are constant (Bottom)
The temperature gradient in snow pack has effects on the microwave signal. The
temperature gets warmer as the snow gets deep. In figure 5.4 first a snowpack with 30cm
depth, 270K temperature, 1.2 mm grain size, and 300kg/m3 density was assumed and its
48 emissivity at each frequency was calculated (red). Then the same snowpack was divided
to three layers where each layer had 10cm depth, 1.2 mm grain size, and 300 kg/m3. The
temperature of the top layer was assumed 268K, the middle layer 269, and the bottom
layer 273. The emissivities calculated for the layered snowpack are lower for 19,22, and
37 GHz and higher for 85GHz (blue).
1
3−Layer
Single layer
0.9
0.8
Emissivity
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
19V
19H
22V
37V
37H
Frequency
85V
85H
Figure 5-4: Emissivity calculated by MEMLS for each frequency. Snowpack was assumed a single layer
(red) and 3-layer (blue)
The MEMLS model has the advantage of being able to calculate emissivity when
the snow has liquid water in it although the emissivity signal loses its sensitivity after
adding 1% of water content (Figure 5.5). The liquid water increases the absorption
coefficient and therefore increases the emissivity. The emissivity reaches 1, after at 1%
water content for 19 and 37GHz and reaches 0.90 for 85GHz. The increase in emissivity
is because the dielectric losses become large and scattering is almost negligible in wet
snow.
49 1
EM19V
EM37V
EM85V
0.9
0.8
Emissivity
Emissivity 0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.5
1
1.5
2
water fraction
Water fraction % Figure 5-5: Emissivity vs. liquid water content fraction where liquid water content varies between 1 and 5
% for 19 GHz, 37GHz, and 85GHz while grain size (1mm), depth (20 cm), temperature (270K), and
density (300kg/m3) stays constant
The ground reflectivity, which is one of the inputs of the model, is the reflectivity at
the ground before adding a snow layer on it (ground-snow interface). The ground
reflectivity is zero if assuming no contribution from ground (below snow layer), however
depending on the vegetation and soil properties the reflectivity varies between 0 and 0.4.
As it was shown in chapter 4 these variation in the ground reflectivity do affect the
microwave signal. Therefore the ground reflectivity (which is 1-emissivity) will be used
as one of the varying inputs of the model.
After examining the model and having the knowledge of how each of the properties
affects the emissivity emission in MEMLS it was decided, for generation of the training
dataset, which properties to vary and which to keep constant and the range of each of
each input properties (Table 5.3). For each combination these inputs the model calculates
a single emissivity for each channel of SSM/I. choosing which parameters from input
snowpack properties and output emissivities to use in the neural network will be
50 explained in section 5-3.
Table 5-3: MEMLS snow emission model input range
Parameter
Snow Depth (cm)
Snow Density (kg/m3)
Min
0
50
Max
300
650
Step
5
50
Snow Grain Size (mm)
0.5
1.9
0.1
Snow Temperature (K)
240
275
5
Ground Emissivity
Water content %
0.6
0
1
5
0.05
1
5.2. Neural Network technique
The inversion algorithm is based on Neural Networks techniques. In the res of this
chapter first the architecture of a neural network followed by specification of the final
neural network used in this study will be describe. Then the neural training steps will be
described, and finally an evaluation of the methodology will done on the results.
The neural network algorithm represents a nonlinear regression tool used to
determine and exploit the general statistical relationship between two quantities. A
classical feed forward Multilayer perceptrons (MLP) is used for this study. MLP consists
of an input layer an output layer, and a variable number of hidden layers. Each layer
contains a number of neurons. The number of neurons in the input and output layer is
determined by the number of inputs and outputs, respectively. The number of neurons in
the hidden layer depends on the complexity of the problem. The input to each neuron in
the next layer is the sum of all its incoming connection weights multiplied by their
connecting input neural activation value. The trainable offset value associated with the
neuron is added to the sum, and the result is fed into the function of the neuron
(activation function). The activation function used here is a non-linear sigmoid function.
The training phase of the neural network is based on the back-propagation learning rule
51 to minimize the mean square error between the desired target vectors and the actual
output vectors. Training patterns were sequentially presented to the network, and the
weights of each neuron were adjusted so that the approximation created by the neural
network minimized the global error between the desired output and the added output
created by the network. The trained neural network can be thought of as a type of nonlinear, least mean square interpolation formula for the discrete set of data points in the
training set. The training phase ends either when a fixed mean square error or a maximum
number of iterations is reached.
The neural network developed for this study is trained using the dataset generated by
MEMLS model. The network was trained and tested more 200 times using different
combination of inputs and outputs, number of hidden layers, maximum iteration number,
and mean square error until it reached a suitable network. The final network was trained
using surface emissivities at 7 frequencies, skin temperature, and ground emissivities at 7
frequencies as its inputs, snow depth, snow density, snow grain size, snowpack liquid
water content as its outputs, and 20 nodes in its hidden layer. The details of how these
inputs and outputs were chosen are explained in the following section. The network was
set to a maximum number of 1000 epoch iteration unless it reaches a mean square error
of 0.0005 for each output. The 15-20-4 network (380 weights) is trained at a rate of 10
seconds per epoch on a laptop. The goal was reached (MSE=5x10-4) after 871 iterations.
The trained neural network is able to retrieve 100 GB of data in less than an hour.
5.3. Neural network training using MEMLS
For training the network with MEMLS, the simulated emissivities and the snow input
parameters were used, as inputs and outputs of the network (i.e. snow parameters
52 employed as input of the model become output parameters of the net, and the
emissivities, being the output of the model, became the input of the neural network)
(Figure 5.6).
In order to generate the training set, snow parameters such as snow depth, snow grain
size, snow temperature, snow density, ground reflectivity, and liquid water content
ranged from a minimum to a maximum value (Table 5.3). Choosing the presented range
of each parameters and their interval was possible only after trying all the possible
combinations of inputs and outputs for the training. 3 different combinations that were
tested are presented here.
Figure 5-6: Neural Network training/testing chart
First the model was fed with a uniform distribution of snow depth, density, snow
grain size, snow temperature. The snow-ground emissivity, and water content percentage
remained 0 (Assuming dry snow and no ground effect). The model then calculated
surface emissivities in 7 channels using the input information of the model. The input
layer of the neural network was assigned to the calculated channels of the emissivity and
the snow temperature used was the same temperature as the model input. One hidden
53 layer was employed with 20 neurons and the output layer was given to be snow depth,
snow density, snow grain size. The learning rule employed a function updating weight
and bias values according to Levenberg-Marquardt optimization (Gill, 1981). Different
variation of parameters were trained and tested until the optimized network was
developed. In order to validate the network, another dataset was generated in the same
way the training dataset was generated (simulated emissivities from MEMLS) but with a
different minimum, maximum, and interval. The input of the validation set was fed to the
trained neural network and retrieved parameters from the network were compared with
the outputs of the validation set. The one showing the lowest RMSE, the highest R2, on
the validation set was selected as best trained network.
Second, to improve the retrieval other capabilities of the model such as water content
percentage and considering a ground-snow emissivity were explored in the process of
generation of training dataset. According to the sensitivity test of the model (figure 5.5)
adding liquid water percentage to the snowpack of more than 2% destroyed the signal.
Therefore, a liquid water percentage between 0 and 2% with a 0.01 step was fed to the
model when calculating the emissivities. The network was trained with the same input
and outputs as before and the retrieved depth from the network showed two different
solutions. The dry depth was validated with a 0.9 correlation with the test data but the wet
snow depth saturates and loses sensitivity as soon as water was added to the snow pack
(figure 5.7). To be able to isolate the wet snow depth from dry snow depth when
retrieving with real data it was decided to retrieve the liquid water percentage. After the
new training the network was able to retrieve the liquid water percentage. Therefor, for
each retrieved point the depth, density, grain size, and liquid water content was available.
54 The points with liquid water content more than zero were considered wet and their depth,
density, and grain size were not considered very accurate.
250
Dry Snow Retrieved depth
Retrieved Depths (cm) 200
150
Wet Snow 100
50
0
0
50
100
150
200
250
Validation depth
Validation Depths (cm) Figure 5-7: Retrieved Depth vs. Test depth for dry and wet snow.
Third improvement to the training was adding ground emissivity information. First
one ground emissivity was added for all the channels and after training and testing it was
decided to add an individual ground emissivity for each frequency. As it was investigated
in chapter 4, figure 4.3 the snow-free ground for each frequency has a different range.
Taking those values into account 7 channels of snow-free emissivities were added to the
inputs of the neural network training. The range for each frequency was chosen according
the real snow-free emissivity values (table 5-4).
One of the capabilities of this model was the fact that it is a multilayered model and
calculates emissivity at each layer. As it was shown in figure 5.4 assuming a temperature
gradient (different temperature for each layer instead of one temperature for the whole
snowpack) affects the final emissivity values. However after training the network and
evaluating it with test data where the test data was single layer, the final retrieved
55 parameters did not change. Also applying real emissivities to the train network (with
multilayer) and network with (single layer) results were very similar. The change in
emissivity values as shown in figure 5-4 is only by 10% which did not make a big
difference in the final retrieval results. Therefore, it was decided not to use a temperature
profile for this work
Table 5-4:Range of snow-free ground emissivity for each frequency for the training
19V
19H
22V
37V
37H
85V
85H
Min
0.69
0.53
0.71
0.72
0.56
0.62
0.57
Max
1
1
1
1
1
1
1
The final network has 15 inputs (7 snow emissivities, 7 snow-free emissivities, 1 skin
temperature) and 4 outputs (snow depth, snow density, snow grain size, liquid water
content). The validation datasets from training was compared with the outputs of the
trained network and all the 4 parameters had high correlation and very low RMSE (table
5-5). The result of the comparison of the test dataset (generated using the MEMLS
model) with the outputs of neural network is shown in table 5-6 which is also in good
agreement
Table 5-5: comparison of training validation dataset with the outputs of the neural network
Depth (cm)
Density (kg/m3)
Grain Size (mm)
Water (%)
R2
0.99
0.99
0.96
1
RMSE
0.01
0.004
0.02
0.3
56 Table 5-6: comparison of the test dataset with the outputs of neural network
Depth (cm)
Density (kg/m3)
Grain Size (mm)
Water (%)
R2
0.92
0.90
0.84
0.93
RMSE
0.76
0.014
0.33
0.5
5.4. Evaluation of the Methodology
5.4.1. Neural Network Jacobian and Uncertainties
The neural network model is trained to obtain good fit statistics for its outputs. There
is a complex relationship linking the inputs to the outputs inside the network and
assessing the physical meaning of this relationship will provide an insight on the
performance and will have better generalization properties. The neural Jacobians can
describe the internal structure of the neural network. The Jacobian, or sensitivities, of a
neural network model are defined as the partial first derivatives of the model outputs with
respect to its inputs. These variables allow one to investigate statistically how a trained
neural network model derives the outputs from the inputs. To evaluate the performance of
this network, its jacobian is calculated. The Jacobian matrix gives the sensitivities for
each retrieved parameter, they indicate the relative contribution of each input
(Emissivities, skin temperature, ground emissivities) in the retrieval for a given output
parameter (Depth, density, grain size, water content). The relation of the inputs and
outputs of a feedforward multilayer perceptron with one hidden layer and a single output
layer (used in this study) is shown in equation 5-2 (Where xi is the input, j is number of
the node in hidden layer (20 nodes in this case), n is the number of inputs (15 in this
case), wij is the input’s weight (15x10) , vjk output’s weight (10x4), and Yk is the output).
The jacobian, which is the derivative of this equation with respect to x, can be expressed
57 using chain rules as shown in equation 5-3. All variables of the equation other than xi are
constant and the derivative of the transfer (hyperbolic tangent, tanh) function is 1-tanh2
(Aires, 2004, Blackwell, 2012). To do the calculation a Gaussian sample of the test
dataset generated by MEMLS was selected and the mean derivative of the datasets was
calculated using equation 5-3.The sensitivity of each of the neural network outputs (snow
depth, snow density, snow grain size, and liquid water content) with respect to the inputs
(emissivities and skin temperature) is shown in table 5.7
From the table 5.7 it can be said that 19V and 85V has the largest affect on depth and
skin temperature has the largest affect on density. 85V mostly affects grain size and 37H
mostly affects the liquid water. It can be concluded that all the channels have some
effects on the 4 retrieved snow properties and hence are essential for the network
training. The 7 ground emissivities, which were used in the training have very small
effect on each individual parameters (less than 0.001) but overall do influence on the
performance of the neural network.
 = ℎ
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=
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!!! !" !
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!
!!! !
!" )!" (5 − 3)
In order to evaluate and test the performance of the trained neural network, the
network was fed with the actual emissivities (from the dataset), their corresponding skin
temperature, and mean snow-free emissivities and the network retrieves the snow
parameters. Then the retrieved snow parameters (depth, density, grain size, water
content), along with the skin temperature and ground emissivities that were used were fed
back to the model (MEMLS) and the surface emissivities at 7 frequencies were calculated
by the model. The 7 calculated emissivities were then compared to the actual emissivities
58 that were used as inputs of neural network (Figure 5.9). As it was shown in figure 5.1 the
depth sensitivity is different for each frequency is 20cm, 150cm, and 400cm for 85GHz,
37GHz, and 19GHz respectively, hence when feeding the retrieved snow depth back to
the model only the range for which the frequency is sensitive is used. For example for
85GHz (figure 5.10.b) only depths less than 20cm were fed back to the model.
Table 5-7: The jacobian of the retrieval output with respect to the inputs
EM19V
EM19H
EM22V
EM37V
EM37H
EM85V
EM85H
Skin Temp
Depth (cm)
18.73
2.27
-3.28
-14.46
-9.61
27.48
-20.44
-26.82
Density (kg/m3)
1.92
-3.20
1.51
-0.03
-1.89
-2.39
2.56
6.44
Grain (mm)
9.30
-16.34
-5.89
-5.79
-2.60
25.44
2.95
0.44
Water (%)
0.60
-1.64
0.49
-1.90
3.15
-0.02
-1.24
-0.44
Figure 5-8: neural network chart
Figure 5.10 shows the difference histogram of the calculated emissivities and actual
emissivities for 19V (5.10.a) and 85V (5.10.b) where 19V has the smallest standard
deviation and 85V has the largest. The distribution of the difference histogram for 19V is
between -0.1 and +0.1 but about 75% of the data are centered on zero (between -0.02 and
59 +0.02) and about 12.5% of data falls on each side the histogram (larger than 0.02 and
smaller than -0.2). The mean is 0.001 and standard deviation is 0.02. To calculate the
depths in this 25% the jacobian table can be used. According to table (table 5.5) the
change in depth to the change in 19V is 18.73. Hence assuming 0.02 change in emissivity
(uncertainty) the change in depth is (0.38cm) on each side of the histogram. The
distribution of the difference histogram for 85V is between -0.2 and +0.2, but about 70%
of the data is between -0.05 and +0.05 and 15% on each side of the histogram (larger than
0.05 and smaller than -0.05). The mean is of 0.007 and standard deviation is 0.06.
Assuming a 0.05 uncertainty, the depth uncertainty for 85GHz is about 1.4cm on each
side.
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
−0.2
−0.15
−0.1
−0.05
0
0.05
19V Emissivity difference
a 0.1
0.15
0.2
0
−0.2
−0.15
−0.1
−0.05
0
0.05
85V Emissivity difference
b 0.1
0.15
0.2
Figure 5-9:Difference histogram of calculated and actual emissivities
There are three possible sources of error in this methodology; 1) input uncertainty 2)
snow emission model uncertainty 3) Neural network uncertainty.
The input uncertainty is derived from the from the surface emissivity data used in the
study. According to (Aires, 2001, Shahroudi, 2014) there is about 0.01 uncertainties in
the emissivity data and 2-3K in skin temperatures. The ground emissivity, which is the
mean of the snow-free emissivity produces about 0.005 uncertainty. Hence there is about
60 0.015 uncertainties in the inputs. The snow emission model produces its own ambiguity.
Durand (2008) characterized the uncertainty of MEMLS radiance predictions by
quantifying model accuracy and sensitivity. It was found that MEMLS was consistent
with the emissivity at 19 and 37 GHz with a bias (mean absolute error) 0.01 for the
vertical polarization and 0.03 for the horizontal polarization. The neural network
produces between 0.02 (for 19Ghz) and 0.05 (for 85GHz) uncertainties
To calculate how much these uncertainties affect the retrieved parameters the
jacobian values (change of each parameters to change of each emissivity channel) are
multiplied by the uncertainty value (change in emissivity). The results (Δ snowpack)
transform the uncertainties in emissivities (ΔEM) to uncertainties in the snowpack
parameters.
Jacobian = Δ snowpack / ΔEM
Then Δ snowpack = ΔEM (uncertainties) x jacobian (from table 5-7)
Table 5-8: Uncertainty of Depth, Density, Grain size, and water content
19GHz
Depth (cm)
Density (kg/m3)
Inputs
0.19
0.02
MEMLS
0.37
0.04
Network
0.56
0.06
Grain Size (mm)
Water (%)
0.09
0.01
0.19
0.01
0.28
0.02
85GHz
Depth (cm)
Density (kg/m3)
Grain Size (mm)
Inputs
0.27
0.02
0.25
MEMLS
0.55
0.05
0.51
Network
0.82
0.07
0.76
Water (%)
0.01
0.01
0.01
In table 5-8 the uncertainty of each parameter is calculated for 19GHz and 85GHz.
The results for the other channels are in between. For the inputs uncertainties an average
61 of 0.01 is assumed. For the MEMLS model uncertainties an average of 0.02 is assumed.
For the Neural network 19V had the smallest (0.02) uncertainties and 85GHz had the
largest (0.05) between all the channels for neural network uncertainties. Thus, an average
of 0.035 uncertainties is assumed for the neural network.
5.4.2. Retrieved Parameters (Snow depth)
The neural network was used to retrieve snow depth using land surface emissivities
(explained in the chapter 3.1) as its input. The land surface emissivities for the whole
Northern hemisphere were used where only the pixels, which were identified as snow
pixels according to the snow detection algorithm in chapter 4, were retrieved. The
distribution of the retrieved depth for 12-snow seasons (1993-2004) is shown in figure
5.11. There are 3 parts, which needs to be investigated in this depth distribution; Depths
below zero (red), which are 35% of the data, depth above 250cm (green), and the peak at
80cm(magenta). The rest (black) have plausible depth values.
First, the negative depths (red) were explored. One thing to check was for wet snow
situations that might have caused the unusual depths. As described before the neural
network retrieves liquid water content besides depth, density, and grain size. The wet
snow pixels were separated (if the liquid water content is more than 0) and examined. It
was found that of all the negative pixels (red) 10% are wet snow pixels. The rest of the
wet pixels had depths larger than 300cm (green). Since it is known that wet snow affects
the microwave signal and it cannot estimated an accurate snow depth all the wet snow
pixels were removed (figure 5.10(b)), After removing the wet snow the negative depths
were reduced from 35% to 25%, the depths above 300cm were disappeared, and the
62 frequency of the depths between 150cm and 300cm was reduced. The wet snow will be
investigated separately later in this section.
Second, since there are still 25% negative, the location of these negative numbers was
examined and it was learned that 15% are ice sheets including Greenland (using the
vegetation type dataset explained in chapter 3). Greenland and ice sheets were removed
and the negative depth dropped from 25% to 10% (total negative depth for the whole
globe and whole 12 years (figure 5.10(c)). At this point the total negative depths were
reduced to 10% and the very large depth were removed.
The third group to investigate was the peak at 70-80cm, which looks odd in the
distribution (magenta). Looking at these pixels closely they only happen during the
month of February of every year and also at same location (North Eurasia). These pixels
are snow-covered during the whole year, which means in February there is fresh snow
over aged snow. Checking the emissivity combination and skin temperature of these
pixels showed that these pixels were identified as snow pixel due to having emissivity
anomaly above 0.05. The skin temperature of these pixels was below 250K (-23C). These
pixels with very cold temperature, which were less than 5% of the whole data, also
caused disagreement in the snow cover comparisons in chapter 4. After investigation they
were flagged as ice according to NOAA cover snow chart and IMS snow ice flag. Adding
a new temperature threshold to the snow detection where the pixels are called snow if
their anomaly emissivity is more than 0.05 and their skin temperature is larger than 250K
removes the peak (figure 5-10(d). These pixels will be considered ice and will be
assigned a depth using interpolation in the next chapter.
63 At this point the depth distribution in figure 5.10(d) is between -50 and 300cm where
most of the depth are between 0 and 60cm, which is a typical depth distribution, except
for the negative part, which is only 10% of the whole dataset. The next step is to
investigate these remaining negative depths.
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
−500
0
Retrieved Depth
0
−500
500
a 1
1
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
Retrieved Depth
c 0
−500
500
500
b 0.9
0
−500
0
Retrieved Depth
0
Retrieved Depth
500
d Figure 5-10: Retrieved depth distribution for snow season 1992-2004, a) all depths, b) Wet snow
removed c) Greenland/ice sheets removed, d) snow pixels with temperature below 250 removed. The negative pixels were examined with all the available information (including
surface type, skin temperature, topography). The 10% negatives could be divided into
two categories, Temperature difficulty (68% of the 10%) and surface difficulty (32% of
the 10%) (Table5-9).
64 Temperature difficulty divides into two categories, close to zero (46% of 68%) and
very cold temperature (22% of 68). Pixels called “close to zero” have a skin temperature
between 268K and 273K. At these temperatures a sudden melt or refreeze happens and
causes a change in the microwave signal and therefore the neural network retrieval. The
pixels called “very cold” have skin temperature less 245K. These pixels have the same
behavior as Greenland, which was removed due to producing negative depths. Figure 511 is all the negative depths of Greenland with their corresponding skin temperature. As
it can be seen most of data has temperature below 250K. Therefore a new temperature
threshold in the snow detection algorithm for pixels with emissivity anomaly difference
above 0.05 was added in a way that if the skin temperature is above 250K and less than
268K the pixels is snow covered otherwise they are flagged as ice. The new threshold
will remove all the negative depths caused by temperature difficulty.
Greenland
4
−200
3.5
Negative Depth
Depths (cm) −400
3
−600
2.5
−800
−1000
2
−1200
1.5
−1400
235
240
245
250
255
Temperature
260
265
270
Temperature (K) Figure 5-11:Negative depth vs. Temperature
Surface difficulty divides into 4 categories, glaciers, open water, rough topography,
and specific vegetation types (table 5-7). For this reason an updated surface type and
topography dataset was used to identify these pixels.
65 First two categories are open water and glaciers. According to Surface type dataset
5% and 7.5 %( of the 32%) are glaciers and open water respectively. Water and ice as
explained before change the emissivity values and this change causes error in the
retrieval. The reason that still water and ice are detected in this dataset is that the original
land water mask which was used to separate open water and ice to produce land surface
emissivities was a 30-year old dataset with 2.5 degree resolution and did not have a
glacier flag. Hence it has missed some of the water and ice (glaciers) pixels whereas the
new surface type used is a new updated version in 0.25-degree resolution with addition of
glaciers (explained in chapter 3).
The third category is rough topography, which covers 8.5% of the 32%. A pixel is
considered rough if the standard deviation of the topography in a 25km pixels is larger
than 150 where only 6% of the whole world has rough topography. Rough topography
causes change in surface slope, which cause a change in the signal incident angle, which
causes change in the emissivity value, which causes an error (producing negative depth)
in retrieval of neural network.
The fourth category, vegetation type is about 11% (of the 32%) and happens when the
vegetation type is mixed forest or cropland. The vegetation effect of each pixel has been
taken into the account when retrieving the neural network by choosing a ground
emissivity (a mean summer snow-free) value when training the network. The vegetation
types in these cases are either cropland or mixed forest. During fall season cropland
ground emissivity is lower than its ground emissivity in summer. Hence the ground
emissivity of real data is different the assumed emissivity in training and causes error in
the retrieval. The mixed forests usually have trees poking out of the snow, which
66 contributes to the total signal and again makes it different from the assumed emissivity
and hence causes an error in the retrieval and produce a negative snow depth in these
cases.
Table 5-9:Negative depths
Close to zero
Very cold
Glacier
Open water
Topography
Vegetation
Temperature difficulty
68%
46%
22%
-
Surface difficulty
32%
5
7.5
8.5
11
The 10% negative depths, which were discussed, are for the whole dataset (all
northern hemisphere for 12 winters 1992-2004). A time series analysis has been done on
these pixels individually to see how many days during a year the pixel is negative and
how many days the pixel is positive. Of all the pixels that have at least one negative day
(10%) during a year only about 3% are negative all the time and about 7% have mixed of
positive and negative depths during a year. The mixed category needs to be investigated
further to see what causes the negative depths. It has been found that the mixed pixels
occur in two scenarios (figure 5.12). 1) Random negative depths days during winter and
spring or, 2) Consecutive depth negative days during fall.
In the first scenario, there are random negative depths between January and April.
The day before and after the negative depth days are positive. It was possible to edit out
all the random negative pixels by smoothing the time series with a 5-day window (5-13).
About 20% of the mixed cases are similar to this case. In the second scenario there are
about 10 consecutive days with negative depths in spring and about 30 consecutive days
of negative depths in the beginning of the fall. About 80% of the mixed cases are similar
67 to this scenario. Figure 5-14 shows the time series of one these pixels with its
corresponding emissivity and skin temperature.
For the 30 consecutive days of negative depth in fall it was observed that the behavior
of the depth is following the behavior of emissivity at 85V. This sudden change in the
emissivity values affects the retrieval of the neural network and causes error in the
produced depth. Therefore, this inaccuracy is due to microwave signal and not the
retrieved network. The reason for this sudden drop in the microwave value could be as
explained before due the their vegetation type (cropland or mixed forest) during fall
season. For the 10 consecutive days of negative depth in spring it was observed that the
skin temperature for these days is approaching to zero centigrade and these cases are due
to the melting/wet snowpack. Since the shown pixel is in very high latitude (North
Canada) it is possible that there was snow at the time.
Daily depth(cm)
50
40
Depth (cm)
30
20
10
0
−10
−20
−30
J
F
M
A
M
J
J
A
S
Days of the year (2003)
O
N
D
Figure 5-12: One pixel time series over a year with mostly positive depth (top) and mix of positive/negative
depth(bottom)
68 Daily depth(cm)
35
30
smoothed Depth (cm)
25
20
15
10
5
0
−5
−10
J
F
M
A
M
J
J
A
S
Days of the year (2003)
O
N
D
Figure 5-13: One pixel time series over a year with mix of positive/negative depth smoothed with a 5 day
window
Daily depth(cm)
20
smoothed Depth (cm)
15
10
5
0
−5
−10
J
F
M
A
M
J
J
A
S
Days of the year (2003)
O
N
D
Daily Emissivity
0.96
19V
85V
0.94
0.92
0.9
0.88
0.86
0.84
0.82
J
F
M
A
M
J
J
A
S
Days of the year (2003)
O
N
D
Daily skin temperature
275
270
265
skin temp
260
255
250
245
240
235
J
F
M
A
M
J
J
A
S
Days of the year (2003)
O
N
D
Figure 5-14: One pixel time series over a year with mix of positive/negative depth with its corresponding
emissivity (19V&85V) and skin temperature
69 5.4.3. Retrieved Parameters (density, grain size, liquid water content)
The developed neural network was able to retrieved snow depth and after evaluating
the performance of the network and removing the unexpected values it was possible to
produce an accurate daily dry snow depth distribution over the Northern Hemisphere.
The other variables that are being retrieved by the neural network are snow density,
snow grain size, and liquid water content. These parameters had less than 5% negative
values, which after removing the negative and high value depths pixels the negative
values for density, grain size, and water content were also removed. The distribution of
these variables is shown in figure 5.15. The Density distribution compare with mean
monthly snow density values derived from Canadian snow course observations which
corresponding to snow climate classes in the Sturm et al. (1995) classification (Brown
and Mote, 2009) is in the right range but there are no pixel by pixel density
measurements to compare the results with. The distribution of grain size according the
literature is accurate, ranging between 0.5 to 2 millimeters depending the age of the
snow.
The liquid water content retrieved from the neural network shows if the snow pixels
are dry (0% liquid water) or wet (more than 0% liquid water). About 15% of the snow
pixels are identified as wet each day in winter and 45% in spring. In order to verify that if
the identification of wet snow is accurate, the depth of the pixels, which were classified
as wet were compared with the corresponding precipitation and skin temperature (figure
5-16). The precipitation data are from the daily global daily GPCP (explained in chapter
3). It is shown from figure 5-16(a) that all the wet snow pixels have precipitation between
1mm/day and 15mm/day. From figure 5-16(b) it can be said that about 60% of the wet
70 pixels with precipitation have near zero temperature (-5 C to +5 C). Hence, about 60% of
the wet snow pixel can be verified as wet due to melting phase (near zero temperature) or
rainfall (TS>-5). The remaining 40% have skin temperature below 265K (-5 C) with
precipitation between 1mm/day and 15mm/day showing there is occurrence of snowfall,
which affects the microwave the signal. Also it can be due to the liquid water content
retrieval uncertainty. More investigation in the wet snow can be done in the future. For
the purpose of this research only dry snow depth was used.
3
Density kg/m
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
a 0
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b 500
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Liquid water content percentage
c 3
Figure 5-15: Retrieved grain size, density, and liquid water content
71 40
7
300
35
6
290
5
280
5
4
25
270
4
20
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temp
precip mm/day
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a 0
100
wet depth
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0
b Figure 5-16: Wet snow vs. a) precipitation b)skin temperature
The neural network retrieval performance was evaluated in this section and all
sources of uncertainty had been investigated. Using the jacobian of the neural network an
uncertainty of 1cm in depth, 0.07 kg/m3 in density, 0.05 mm in grain size, and 0.01% in
water content was estimated for the methodology. The retrieved values from the network,
which had negative values, were investigated and was found that most of the negative
values are due wet snow and ice ground. A correct range of each of the retrieved
parameters is represented. To validated the accuracy of these values in the following
chapter a comparison with other datasets will be conducted.
72 6. Results
The retrieved dry snow depth (excluding the negative depths) was mapped for the
northern hemisphere (Figure 5-1) for the month December 2003. The range is between 0
and 90 centimeters for dry snow. The white parts are locations where the retrieval
identified the snowpack as wet. The average daily coverage of dry snow is about 56% of
the Northern Hemisphere.
Figure 6-1:snow depth map
6.1.1. Comparison retrieved snow depth with CMC and Chang algorithm
A comparison between retrieved depth and Chang snow depth algorithm has been
applied to the data over the whole northern hemisphere and winter seasons of (20002004) (figure 6.2). Chang proposes that there is straightforward relationship between the
volume of snow crystals present in the snow pack, and hence, SWE or snow depth, and
the degree of microwave scattering by ice grains, measured by the drop in the brightness
temperature (TB) observed by the satellite at a specific microwave window frequency.
The degree of scattering can be measured by computing a Scattering Index as the positive
73 difference in TB measured at two microwave frequencies. The algorithm has been
developed for SMMR originally and is the difference between TB18H-TB36H.
Armstrong (2001) modified this for SSM/I with 19H and 37H (equation 6-1). The
retrieved depth and Change depth are in a good agreement with correlation of 0.90 and
RMSE of about 15 cm.
retrieved depth
SD (cm)=1.59 TB (19H-37H)
(6-1)
90
9
80
8
70
7
60
6
50
5
40
4
30
20
3
10
2
20
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60
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Chang depth
100
120
Figure 6-­‐2: Retrieved Depth vs. Chang Algorithm Then the retrieved depth was compared with CMC snow depth (figure 6-3). There is
little structure between the two datasets. The retrieved depth is between 0 and 140cm
while the CMC depth stays below 40cm. As explained in the data section the CMC snow
depth takes the available snow depth point measurement from stations around globe and
uses a method of optimum interpolation with an initial guess field provided by a simple
snow accumulation and melt model using analyzed temperatures and forecast (six hour)
precipitation from the CMC Global Environmental Multiscale (GEM) forecast model. In
regions where there are no observations of snow depth, the snow depth shown in the
analysis corresponds to the initial guess field. The model as mentioned in other literature
74 (Brown and Brasnett, 2010) is not very accurate therefore only the initial point
measurement of the snow depth is used instead of the modeled snow. The point
measurements were matched with the 25km SSM/I pixels and only 10% of the whole
CMC data had real values measured at the station. The stations were matched with the
25km emissivity resolution and will be called “edited CMC” from now on. Figure 6-4 is
the comparison between the retrieved depth and “edited CMC” depth. This time a
structure can be seen in the 2D histogram although still the CMC depth are much lower
than the retrieved depths. The correlation is: R2=0.27 and RMSE=30cm in this
comparison.
140
10
120
9
8
retrieved depth
100
7
80
6
60
5
4
40
3
20
2
0
0
20
40
60
80
cmc depth
100
120
140
Figure 6-3:Retrieved depth vs. CMC depth
140
6.5
120
6
5.5
100
retrieved depth
5
4.5
80
4
60
3.5
3
40
2.5
2
20
1.5
0
0
20
40
60
80
cmc depth
100
120
140
Figure 6-4 Retrieved depth vs. edited CMC depth
75 The edited CMC was compared with the Chang snow depth and as expected it also
had a low correlation 0.3 with 27 cm RMSE (figure 6-5). The very low values of CMC
depth in comparison with retrieved snow depth looks suspicious and needs more
investigation.
100
90
7
80
6
Chang depth
70
60
5
50
4
40
30
3
20
2
10
0
0
20
40
60
80
CMC depth
100
120
140
Figure 6-5: Edited CMC depth vs. Chang depth
To look more deeply into the CMC values, the time anomaly of the edited CMC
depth and retrieved depth (the mean of the time record of each pixel subtracted from that
pixel) were compared and the correlation increased to 0.4 and the RMSE decreased to
25cm. Another comparison was done in a way that the depth of one area with terrain and
short vegetation, i.e. grassland, over time (winter seasons of the whole record) was
chosen to investigate. The pixels with grassland vegetation were matched in time and
space for retrieved depth and edited CMC. A 5-day high pass filter was applied to the
long-term anomalies for both datasets in order to remove low frequencies variability such
as interseasonal and interannual variability. The results were compared in a scatterplots
(figure 6.6). This time a linear structure can be seen in the plot, the correlation has
increased to 0.6 and the RMSE decreased to 20cm.
76 60
55
3
50
Retrieved Depth
45
40
2.5
35
30
2
25
20
1.5
15
10
10
20
30
40
CMC Depth
50
60
Figure 6-6:edited CMC vs. Retrieved depth for grassland over time. Low frequency variation removed by
applying a 5-day high pass filter.
6.1.2. Snow water equivalent (SWE)
One climatological and hydrological objective of snow studies is to estimate Snow
water equivalent (SWE) globally over a long time. The accuracy of SWE information is
currently limited as the level of SWE can be only assessed by interpolating observations,
typically sparse both spatially and temporally, from gauging networks and snow courses,
or by interpolating daily synoptic weather station-based point-wise SD or precipitation
information. Chang has also an empirical SWE algorithm for microwave, which has been
used for three decades (equation 6-2). From the Results of the neural network Snow
depth and Snow density for each pixel are available it was possible calculate SWE
(Equation 6-3). The estimated SWE was compared with Chang SWE algorithm (figure 67). The comparison shows a good agreement with a correlation of 0.8 and RMSE
200mm. There are a group of SWE, which by the Chang algorithm they are between 0
and 50mm but by the estimated SWE from retrieved parameters are between 100 and
300mm. This amount is only 5% of the whole dataset (12 year of winter season and all
the snow pixels of the northern hemisphere). Comparing this figure with figure 6-2 where
77 the retrieved snow depth was compared with Chang snow depth this shape did not exist.
Hence this group came in after introducing the density parameters. Assuming the Chang
algorithm as truth, this disagreement could be due to the retrieved density uncertainty.
However the Chang algorithm itself is know to underestimate SWE in high latitudes
(Armstrong 2002), meaning it is possible that the estimated SWE is more accurate than
Chang algorithm. To prove this, a validation of the retrieved density measurements is
required although there is not enough density measurement for this validation.
SWE (mm)=4.8 mm /K * TB (19V-37V)
(6-2)
SWE (mm) =Depth (cm) *10 * density (kg/m3)/1000(kg/m3)
(6-3) 300
5
4.5
250
4
3.5
retrieved SWE
200
3
150
2.5
2
100
1.5
1
50
0.5
0
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100
150
Alg SWE
200
250
300
Figure 6-7: Estimated SWE vs. Chang SWE algorithm
0
6.1.3. Interpolation
After investigating what are the causes of all the negative depths instead of removing
them from the dataset it is possible to generate a value for some of these pixels where the
occurrence of negative depths are relatively rare, by interpolating temporally or spatially.
Figure 6-8 is an example of a pixel that has few days of negative depths in March and
78 October. The negative depths are 2 days in in February (4th to 6th), 20 days in March (1st
to 20th), and 29 days in October (1st to 29th). Possible exploitations for negative values
were discussed in chapter 5. In order to choose values for these days the mean of last day
with positive depths before the negative depths and the first day of positive depth after
the negative depths was used. In this example the 2 days in February was filled with
11cm, the 29 days in October was filled with zero, and the 29 days in March was filled
with 7cm. Another way of filling these values is by applying a 7-day time average
window to time-series to remove the low (negative) depths. When there are only a couple
of days of negative values (not consecutive) this method might be more efficient. To
compare the 2 methods figure 6-9 shows some negative depth days in January and
February. In figure 6.9-a the interpolation is applied to time series and in figure 6-9-b a 7day filter is applied to the time series. Applying the time average filter removes the
negative values, however, it also removes some of the daily variations that might be real
(due to snowmelt/snowfall). Therefore the interpolation method was applied to the
missing data (wet snow, negative depths, negative density, and negative grain size) for all
the pixels in the northern hemisphere and the whole time record (1993-2004).
70
60
50
Snow Depth
40
30
20
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−20
J
F
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Figure 6-8: Time series of 1 pixel where the negative depths interpolated
79 Interpolation
Snow Depth
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Snow Depth
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DOY 2003
Figure 6-9: Time series of 1 pixel for one year where the negative depths a)interpolated and
b)time averaged
6.1.4. Interannual Variability of snowpack parameters
One of the reasons to have an accurate measurement of snow depth is to study the
interannual variation of the snow depth in order to understand its impacts on the climate.
The time series in Figure 6.10 shows the mean snow depth for each day in the Northern
Hemisphere, for the retrieved snow depth, CMC snow depth, and Chang snow depth. As
also seen in figure 6.2 the retrieved depth and the Chang depth have similar values and
follow the same behavior whereas the CMC depth has lower values. However all the
three dataset show the same seasonal variation and interannual changes. Both maximum
snow depth and minimum summer time snow depth increase between 2002 and 2004. In
2001 there is 10% drop in snow depth, which also happened in the snow cover time series
(figure 4-7). As discussed in chapter 4 (section 4.4) this sudden decrease is associated
with a sudden increase of TS in that year.
80 Depth
40
Retrieved
CMC
Chang
35
30
25
20
15
10
5
0
2001
2002
2003
DOY 2001−2004
2004
Figure 6 10: Time series of mean depth for retrieved depth,
CMC depth, and Chang depth for 2001-2004
Figure 6-10 shows a comparison of the three datasets from 2001 to 2004, which was
the overlap time between the retrieved snow depth and CMC snow depth. However the
emissivity data are available from 1993 to 2004 therefor the retrieved parameters from
the neural network can be shown for this time period. Figure 6-11 is the time series for
the mean retrieved snow depth, mean retrieved density, mean retrieved grain size, and
mean SWE (estimated and algorithm) for each day.
The Chang SWE as shown before has lower values than estimated SWE for the
summertime minimum. Over the winter of 1993 to 2000 the Chang has also lower SWE
but after 2000 they have the same high peak as the estimated SWE. The Chang algorithm
is known for underestimating SWE but their measurement method was modified after
2001 (Brown and Brasnett, 2010), which agrees with this figure. The retrieved algorithm
is using 85Ghz where the Chang algorithm is using 37GHz. 85GHz is known for being
able to see shallow snow, hence the minimum summertime with shallow snow are
estimated more accurately with the retrieved algorithm.
81 The depth and SWE time series show that there is an increase in amount of snow
between 1995 and 1998 at their minimum and after 2001 an increase in the amount of the
snow both at their minimum and their maximum. More investigation of the day-to-day
variation of the snow depth and SWE can be done in the future.
The time series of depth and density are consistent with the SWE time series and have
a reasonable range, suggesting there is no systematic error in the retrieval. From the
density and grain size time series it can be said that the two parameters are not constant
as the depth is changing (which is the assumption of the Chang algorithm). Also the
retrieved depth is multiplied by the assumed constant density suggested by Chang
algorithm instead of by the retrieved density. This SWE in comparison with the estimated
SWE (where both depth and density are retrieved) has removed some of the daily
variations suggesting the density does varies with different depths. Therefore for SWE
retrieval it is essential to have all the possible snowpack properties and surface
information for each pixel.
82 Depth
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10
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
DOY 1993−2004
Density
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1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
DOY 1993−2004
Grain Size
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1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
DOY 1993−2004
SWE
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SWE
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Estimated SWE
Chang SWE
0
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
DOY 1993−2004
200
Figure 6-11: Time series of mean snow depth, mean density, mean grain size, and mean SWE
150
100
50
0
1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004
DOY 1993−2004
83 80
SWE w/retrieved density
SWE w/constant density
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(c) Figure 6-­‐12:SWE Time anomaly (2003) for SWE=Retrieved Depth x Retrieved Density (blue) and SWE=Retrieved Depth x Constant Density (red). a) Evergreen forest b) Tundra c) Deciduous Forest In order to check how much having the retrieved density instead of a constant density
affects the SWE product, the SWE was estimated in two different ways and were
compared to each other (figure 6-12). The figure shows the time anomaly of the SWE.
SWE1 = retrieved Depth x retrieved density
SWE2 = retrieved Depth x constant density (change algorithm constant 300kg/m3)
The comparison shows that in some areas such as evergreen and deciduous forest the
variation of density matters and affects the behavior of SWE (6-12 b & c) but in some
84 areas such as Tundra (6-12 a) this variation is very small and negligible. The mean
density estimates used in Change algorithm is 300 kg/m3 where the mean retrieved
density for Tundra (296kg/m3), Evergreen (170kg/m3), and Deciduous (192 Kg/m3) is
different, showing that assuming a constant density for the all vegetation is not accurate.
Hence, having the retrieved density, which will improve the SWE estimates.
85 7. Conclusions
The main objective of this study was to improve SWE measurement using passive
microwave and produce a SWE time record for climate studies. To do this in the first
part of this study the snow signature was isolated from the microwave signal (Chapter 4).
In the second part an inversion method was applied to a snow emission model to retrieve
snowpack properties using the snow signature (Chapter 5). And then the snowpack
properties, which include snow depth and snow density, were used to estimate SWE.
Many snowpack retrievals and inversion methods have been proposed to estimate SWE
from passive microwave but the main advantages of the present method in this study are:
1) The passive microwave dataset which was used in the retrieval does not have the effect
of atmosphere and surface skin temperature variability, 2) The method uses all the
channels and is able retrieve physically consistent multi-variables (depth, density, grain
size, liquid water content), and 3) The method is based on a physical method (radiative
transfer model) directly.
The effective emissivity product used in this analysis has the advantage of having the
contributions of the atmosphere, including clouds and water vapor, removed and the
physical temperature variations separated from the effective emissivity variations.
Although this particular dataset is produced under clear sky (cloudy pixels are removed),
it should work when there is cloud if it is not precipitating (Aires et al., 2001]. By
employing a difference of effective emissivities at low and high frequency and
determining the time-anomaly of this difference for each location, the constant effects of
land surface vegetation properties were reduced leaving only the signal with the snow
signature. An algorithm to detect snow with the new signature was developed using an
86 anomaly emissivity difference (δEM19-85) of 0.05 as its threshold. The snow detection
results agreed about 78% with another microwave snow detection (NISE) and more than
80% of the time, with three other snow datasets (IMS, MODIS, CMC). The best
agreement (92%) was with MODIS, which is an IR/Visible product. Most of the 10%
disagreements between the proposed algorithm and other snow cover products can be
explained by rapid melt-freeze-refreeze events, contamination by coincident precipitation
mislabeled frozen ground, and spatial/temporal mismatches. The remaining unexplained
cases represent only about 1% of the dataset. These disagreements point to the need for a
high time resolution product that is not limited by cloud cover or solar illumination,
especially to detect the rapid melt/freeze events. Also, if precipitation effects were
accounted for then such a product would capture changes in the surface following
snowfall (or rainfall) events. The cases of bare ice cover or snow cover on permanent ice
require more careful study to determine whether the microwave can detect the changes.
After isolating the snow signature from the microwave signal, the signature (with
only snow effect) was used to retrieve snowpack properties. This was done by inverting
the snow emission (MEMLS) model equation based on neural network techniques. The
model takes snowpack properties as its input and calculates simulated emissivities. These
simulated emissivities and the snowpack properties were used to generate training and
testing datasets for the neural network. All 7 channels of the emissivities were used in the
training plus 7 channels of ground emissivities to consider the snow-free (ground
emissivities). Skin temperature from the inputs of the model was also used as an input of
the neural network. The snow depth, snow density, snow grain size, and liquid water
content, which were all the inputs of the model were used as the targets (outputs) of the
87 neural network. Liquid water fraction was used in the retrieval since the model has the
advantage of considering wetness. After training the network with the model-generated
properties it was used for actual retrieval. The microwave surface emissivities (Pixels that
were identified as snow), the skin temperature (IR), and the ground emissivities
(emissivities of the snow-free pixel) were used as the inputs of the neural network. The
neural network was able to retrieve snow depth, snow density, snow grain size, and liquid
water content of the snowpack.
To evaluate the performance of the network and estimate the uncertainties related to
the network the jacobians were calculated. The neural network jacobian, which shows the
sensitivity of each output to each input, verified that all the channels for the retrieval are
needed. There are three sources of uncertainties in this method, the inputs, the emission
model, and the neural network. The overall uncertainties for all these three sources are
between 0.01 and 0.05 (as a change in emissivities) depending on frequency channel.
With the jacobian it was possible to translate these emissivity uncertainties to snowpack
properties uncertainties. Snow depth is less than 2cm, density is about 0.1 kg/m3, grain
size is about 1mm, and liquid water fraction is about 0.1%.
Further evaluation of the network showed that the network is able to retrieve dry
depth accurately but when liquid water content appears in the snowpack the retrieved
depth is very not accurate. It was shown that all the pixels, which were identified as wet
snow by the retrieval, also have precipitation on that day and matched location. 60% of
these pixels also have a temperature near zero, which means the pixel was likely melting
phase or the precipitation was in form of rain. The wet snow depths were removed from
the results and require further investigation.
88 More investigation on the retrieved depths showed that melt/freeze cycle, ice cover
ground, rough topography, mixed scenes, and cropland vegetation type influence the
retrieval by causing a large changes in the emissivity values not associated with snow.
The change in emissivity causes change in the retrieval and therefore produces a negative
snow depth. However, these values are only 10% of the whole datasets. The time series
of these pixels showed about 7% of the 10% have positive depths for most of the days
during the year and only have negative for a few days during the year.
These negative values and the wet snow were removed from the results and a
temporal interpolation was applied to data to fill the missing days. After applying the
interpolation a daily snow depth, snow density, and snow grain size is available for the
northern hemisphere.
A comparison of snow depth with Chang algorithm showed a 0.9 correlation. In
comparison with CMC (station data) the retrieved depth had higher values, however the
CMC data are known for underestimating snow and not being accurate. The CMC data
were edited in way that only the station data with real snow depth measurements were
used. Taking a time anomaly and applying a 5-day high pass filter to the CMC data
improved the comparisons between CMC and the retrieved depth.
Having snow depth and snow density it was possible to estimate SWE. An
interannual variability of the retrieved snow depth and SWE between 1993 and 2004
showed an increase in the amount the snow in the last 4 years (2001-2004).
One improvement in this method is that the retrieved depth is using all the emissivity
channels especially the 85GHz that can see shallow snow. Other snow algorithms use
only two channels in their retrievals and avoid 85 GHz because it is more affected by the
89 atmosphere. This could be one reason that in summertime the retrieved depth sees higher
snow depth.
Another improvement is that the method retrieves multiple variables (depth, density,
grain size). In other words the method is not assuming the other snowpack properties as
constant, which is the assumption in other algorithms. It was shown that the variation of
density and grain size can affect the retrieved depth and estimated SWE .
The fact that the contribution of atmosphere, temperature, and underlying surface in
the microwave signal has been taken into account for this method is an improvement over
other snow products, which are not considering these contributions.
This neural network was able to produce an accurate long-term (1993-2004) snow
product (snow depth, snow density, snow grain size, SWE) for the northern hemisphere.
This time record can be used in climatology studies. The method can still have more
improvements, which will be discussed in the next chapter.
90 8. Future Works
One possible future investigation is to improve the proposed methodology in this
work. One way to improve this methodology to validate the results is to compare the
retrieved parameters with actual measurements of snowpack. The CREST-SAFE project
which its long-term record includes microwave measurements, depth, density, grain size,
and the radiometric is an option for a comparison for future studies.
Another way of improvement is to reduce uncertainties. As discussed before there are
three sources of error in this methodology; 1) Inputs (emissivities and skin temperature)
2) Snow emission model 3) Network. Input error is due to the emissivity values
inaccuracy. Model error is due to how well the model calculates the emissivity using the
given parameters. The network error was evaluated and it was concluded that it affects
the depth less than 2 cm and the density about 0.1 kg/m3.
The emissivity data as explained before are derived from SSM/I using a neural
network. The quantification of the dataset calculated about 0.01 uncertainties for this
datasets (Aires, 2001). However, the ancillary datasets (such as atmosphere- temperature
profile, the IR skin temperature, land/water mask, etc.) used to estimates these
emissivities may cause some of the errors. Also these emissivities are for clear sky only,
which covers about 56% of the Northern Hemisphere. Aires et al. (2001) showed that the
cloudy emissivity values are similar to the clear sky emissivity values and the
emissivities can be re calculated taking cloudy pixels into account to have larger
coverage of Northern Hemisphere. Therefore an improved emissivity datasets to use as
the inputs of the neural network will help improve this methodology.
91 The MEMLS model used in this study to train the neural network uses certain inputs
and radiative transfer equations to calculate the simulated emissivities. These calculated
emissivities are not always the same as the actual emissivities values with a given inputs
value because the model does not take into account the vegetation and scene type. For
example, rough topography and mixed scene causes a change in actual emissivity values
whereas the model does not take these into account when calculating emissivities.
Therefore there will be a difference between emissivities used in training and emissivities
used in retrieval. Hence, another improvement can be the use of another emission model,
which takes into account these other contributions. In conclusion having a better snow
emission model and more accurate inputs (emissivities) will improve the performance of
the retrieval and having data to compare the results with will help evaluating the results
better.
Since the objective of this study was to produce SWE records for climatology studies
and at the end of this study a long-term daily SWE product was produced, the next thing
to is to use this record for that reason. For example there is a relationship between flash
flood and snow water equivalent and examining and studying the interannual variation of
SWE will benefits the flood forecasting techniques.
92 9. References
Adler, R. F., et al. (2003), The version-2 global precipitation climatology project (GPCP)
monthly precipitation analysis (1979-present), Journal of Hydrometeorology, 4(6), 11471167.
Aires, F., C. Prigent, W. B. Rossow, and M. Rothstein (2001), A new neural network
approach including first guess for retrieval of atmospheric water vapor, cloud liquid
water path, surface temperature, and emissivities over land from satellite microwave
observations, Journal of Geophysical Research-Atmospheres, 106(D14), 14887-14907.
Aires, F., C. Prigent, W.B. Rossow (2004), Neural network uncertainty assessment using
Bayesian statistics with application to remote sensing: 3. Network Jacobians, Journal of
Geophysical Research, 109.
Andreadis, K. M., D.P. Lettenmaier (2006), Assimilating Remotely Sensed Snow
Observations into a Macroscale Hydrology Model, Adv. Water Res., 29, 872-886.
Armstrong, R. L. and M. J. Brodzik. 2001. Recent Northern Hemisphere Snow Extent: A
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